If you are purely a designer (and not contracted for the daily operation of the site), the answer is "no".
GDPR Article 4 defines the "roles" responsible for complying with GDPR, and there are two: Controller and Processor. The Controller is the one who calls the shots. In particular: Decides what personal data to process. This is usually the owner of the web site. The Processor is the one that actually does the processing. This is usually some company providing some sort of data processing service (e.g. SaaS, PaaS, etc.). The relationship between the Processor and the Controller must be contractual. The contract is called a DPA (Data Protection Agreement or Data Processing Addendum).
As a designer, you don't fit into any of these roles. If your contract with the client is silent on liability for GDPR compliance, then you have no liability.
This goes for projects completed both before and after the May 25 deadline.
Of course, if there are GDPR clauses in your contract, then you must fulfil them just as have to fulfil any other contractual obligation. But unlike the controller and the processor, there are no automatic legal liability for a designer or programmer.