“Serious harm” is a requirement in the Defamation Act 2013
The Supreme Court interpreted it in Lachaux v Independent Print Ltd & Anor  UKSC 27 (12 June 2019) at [10-20]:
... it not only raises the threshold of seriousness above that envisaged in Jameel (Yousef) and Thornton, but requires its application to be determined by reference to the actual facts about its impact and not just to the meaning of the words.
You, as the plaintiff must prove on the balance of probabilities that you have or are likely to suffer serious harm. That is harm that is greater than the previous common law threshold of substantial.
In this case, the court agreed that serious harm had been done so it’s useful to consider what Lord Sumption said about the evidence that had (correctly) convinced the trial judge at  (my emphasis):
On the footing that (as I would hold) Mr Lachaux must demonstrate as a fact that the harm caused by the publications complained of was serious, Warby J held that it was. He heard evidence from Mr Lachaux himself and three other witnesses of fact, and received written evidence from his solicitor. He also received agreed figures, some of them estimates, of the print runs and estimated readership of the publications complained of and the user numbers for online publications. He based his finding of serious harm on (i) the scale of the publications; (ii) the fact that the statements complained of had come to the attention of at least one identifiable person in the United Kingdom who knew Mr Lachaux and (iii) that they were likely to have come to the attention of others who either knew him or would come to know him in future; and (iv) the gravity of the statements themselves, according to the meaning attributed to them by Sir David Eady. Mr Lachaux would have been entitled to produce evidence from those who had read the statements about its impact on them. But I do not accept, any more than the judge did, that his case must necessarily fail for want of such evidence. The judge’s finding was based on a combination of the meaning of the words, the situation of Mr Lachaux, the circumstances of publication and the inherent probabilities. There is no reason why inferences of fact as to the seriousness of the harm done to Mr Lachaux’s reputation should not be drawn from considerations of this kind. Warby J’s task was to evaluate the material before him, and arrive at a conclusion on an issue on which precision will rarely be possible. A concurrent assessment of the facts was made by the Court of Appeal. Findings of this kind would only rarely be disturbed by this court, in the absence of some error of principle potentially critical to the outcome.
So, you must prove that it is likely that prospective employers/schools will see the defamatory statements and that they are so grave that it is likely that you would be refused a position because of them.