Costa was the first, but not the leading, case. Internationale Handelgesellschaft is. See below. I assume you're asking about EU law's supremacy over UK law, as you tagged [united-kingdom].
4.2 The scope and implications of the supremacy principle
Although Costa clearly established the principle of supremacy of EU law, questions
remained about its precise scope and implications. Subsequent case law clarified two
First, in Simmenthal, the CJEU addressed the implications of the supremacy principle
for national courts.88 The case arose from an Italian law requiring meat importers to pay for veterinarian checks at the national border. Although it was established
that this was contrary to directly effective EU law concerning the free movement
of goods, the Italian government argued that domestic courts could not order it to
repay the fees until and unless the Italian Constitutional Court annulled the law in
question. This view did not find favour with the CJEU, which took the opportunity
to spell out the practical consequences of the supremacy doctrine for domestic courts
faced with incompatible national laws. The CJEU said it was the task of national
courts to protect the rights conferred upon individuals by EU law.89 Domestic courts
therefore had to ‘apply [Union] law in its entirety’, disregarding ‘any provision of
national law’—whenever enacted—‘which may conflict with it’, and ignoring any
national rules that, if applied, would compromise domestic courts’ capacity to do the
Second, in Internationale Handelsgesellschaft, the CJEU held that the principles
laid down in Simmenthal applied to all types of national law, including provisions
of member states’ constitutions, and including provisions in such constitutions concerning
the protection of human rights.91 It was therefore the duty of national courts
to disapply national constitutional human rights guarantees to the extent that EU law
was inconsistent with them. Unsurprisingly, this conclusion provoked a good deal of
disquiet, but the Court was careful to say that such situations should arise rarely (if at
all). This was because EU law itself recognised the fundamental rights common to the
constitutional traditions of member states. As a result, the Union was bound by those
rights and powerless to legislate or otherwise act in breach of them.92 It would therefore
rarely, if ever, be the case that a national court was forced to choose between a
national human rights law and a valid EU provision.
88 Case 106/77 Amministrazione delle Finanze dello Stato v Simmenthal SpA  ECR 629.
89 Simmenthal, . 90 Simmenthal, –.
91 Case 11/70 Internationale Handelsgesellschaft mbH v Einfuhr- und Vorratsstelle für Getreide und
Futtermittel  ECR 1125.
92 Case 4/73 J Nold Kohlen- und Baustoffgrosshandlung v Commission of the European Communities
 ECR 985. See further Tridimas, General Principles of EU Law (Oxford 2005), ch 7.
Mark Elliott, Robert Thomas. Public Law 2020 4 edn. pp 380-1.
The validity of Union law could thus not be affected – even by the most fundamental
norms within the Member States. The Court’s vision of the supremacy
of European law over national law was an absolute one: ‘The whole of
[European] law prevails over the whole of national law.’15
15 R. Kovar, ‘The Relationship between Community Law and National Law’, in EC
Commission (ed.), Thirty Years of Community Law (EC Commission, 1981), 109 at 112–13
Robert Schutze, European Union Law 2018 edn, p 124.
(B) Ambit: Supremacy Applicable Against All National Law
While the conceptual basis for the supremacy of EU law was set out in Costa [that you mooted in your post], the ambit of the principle
became clearer in later decisions. In the following case, the Court ruled that the legal status of a conflicting national measure was not relevant to whether EU law should take precedence.3 Not even
a fundamental rule of national constitutional law could be invoked to challenge the supremacy of a
directly applicable EU law.
This ruling gave rise to a potentially serious conflict in the relationship between the German
Federal Constitutional Court and the ECJ. While the latter has sought to avoid a direct constitutional
conflict with a national court,4 it has never retreated from its claims.
Case 11/70 Internationale Handelsgesellschaft mbH v Einfuhr- und Vorratsstelle für Getreide und Futtermittel  ECR 1125
The applicant argued that a Community regulation under which a deposit would be forfeited if the
goods were not exported within the period of time set was contrary to principles of national constitutional
law, including freedom of action and of disposition, economic liberty, and proportionality.
- Recourse to the legal rules or concepts of national law in order to judge the validity of measures
adopted by the institutions of the Community would have an adverse effect on the uniformity and efficacy
of Community law. The validity of such measures can only be judged in the light of Community
law. In fact, the law stemming from the Treaty, an independent source of law, cannot because of its
very nature be overridden by rules of national law, however framed, without being deprived of its character
as Community law and without the legal basis of the Community itself being called into question.
Therefore the validity of a Community measure or its effect within a Member State cannot be affected
by allegations that it runs counter to either fundamental rights as formulated by the constitution of that
State or the principles of a national constitutional structure.
The Court faced the opposite kind of argument in Ciola, where the Austrian Government argued
that the principle of primacy should not automatically apply ‘to specific individual administrative
acts’.5 The Court dismissed this argument, reaffirming that any provision of national law that
conflicted with directly effective EU law should not be applied. Thus, the principle of primacy is
required whenever directly effective EU law is concerned, and regardless of whether fundamental
national constitutional norms, or minor administrative acts, are at issue. The Court, however, qualified
Ciola by admitting that, under specific circumstances, supremacy needs to be accommodated
with domestic limitations of the period of time during which administrative acts may be repealed
or judicially contested.6
3 See also Case C–473/93 Commission v Luxembourg  ECR I–3207, ; Case C–273/15 ZS ‘Ezernieki’ v Lauku
atbalsta dienests EU:C:2016:364, ; Case C–516/17 Spiegel EU:C:2019:625, ; Case C–476/17 Pelham EU:C:2019:624, .
4 See, eg, Case C–446/98 Fazenda Pública v Câmara  ECR I–11435, –.
5 Case C–224/97 Ciola v Land Vorarlberg  ECR I–2517, .
6 Case C–453/00 Kühne & Heitz  ECR I–837; Case C–2/06 Willy Kempter AG  ECR I–411. See Ch 14 for
Op cit, pp 316-7.
Why must I know which Member State you're asking about, to best answer your question? Because
There is a continuing
tension between national accounts of EU law and the CJEU’s account. Constitutional conflicts
continue to arise in specific cases, and it remains for national courts to resolve cases arising before them
involving a conflict between EU and national law.46 Reasons of space preclude detailed consideration of
all Member States. The ensuing analysis therefore focuses on five Member States, Germany, Italy, France,
Poland, and the Czech Republic, thereby including an admixture of original signatories and states that
46 M Claes, The National Courts’ Mandate in the European Constitution (Hart, 2006); A-M Slaughter, A Stone Sweet,
and J Weiler (eds), The ECJ and National Courts: Doctrine and Jurisprudence (Hart, 1998); K Alter, Establishing the
Supremacy of European Law: The Making of an International Rule of Law in Europe (Oxford University Press, 2001); N
Walker (ed), Sovereignty in Transition (Hart, 2003).
Here's how Supremacy of EU Law works for UK Post-Brexit. I quote some salient paras. from pp 363-4.
i. The principle of the supremacy of EU law in relation to the UK is dealt with in sections 5 and
6 of the European Union (Withdrawal) Act 2018, EUWA, as amended by the European Union
(Withdrawal Agreement) Act 2020. The position is as follows.
ii. First, section 5(1) EUWA provides that the principle of the supremacy of EU law does not apply
to any enactment or rule of law passed or made on or after the end of the implementation period,
which is 31 December 2020, known in the legislative jargon as IP completion day. This is in
accord with the logic of UK withdrawal from the EU.
iii. Secondly, section 5(2) EUWA then provides that ‘accordingly, the principle of the supremacy of
EU law continues to apply on or after IP completion day so far as relevant to the interpretation,
disapplication, or quashing of any enactment or rule of law passed or made before IP completion
day’. It means that if there is a conflict between pre-IP completion day domestic legislation
and retained EU law, the latter takes precedence. It also means that pre-IP completion day
domestic law should be interpreted, as far as possible, in accordance with retained EU law. The
policy rationale underlying section 5(2) is legal certainty: prior to IP completion day, EU law had
supremacy over domestic law, and it was felt that this should therefore continue.
vii. Thirdly, section 5(1) EUWA is further qualified by section 5(3). It provides that section 5(1) ‘does
not prevent the principle of the supremacy of EU law from applying to a modification made on
or after IP completion day of any enactment or rule of law passed or made before IP completion
day if the application of the principle is consistent with the intention of the modification’. The application of this qualification can clearly be contestable, and the issue may well have to be
decided by the UK courts in the light of the evidence that is available from Parliament, which is
admissible in court.