They would have to bring it before Parliament and it would have to go through Parliamentary process. It could be a private member’s bill or part of the government programme, so theoretically they could.
The problem with this course of action is, I think, that the SC judgement laid out comprehensively why a gender certificate definition of sex made the Act and therefore inequalities legislation incoherent, and it is difficult to see how this incoherence could be addressed. The SC judgement gives multiple examples of why revised legislation to include certified sex would not work (here, I don’t mean this is explicitly what they say but in working through what it would mean for the provisions if having a GRC was included in the definition of sex, they show the issues). I have stepped away from this issue over the last couple of days but I am not aware that anyone has seriously refuted the reasoning of the judgement rather than just railed/wailed against it.
The only way would be to remove sex completely as a protected characteristic much as the way Scotgov decided not to have misogyny in the hate crime legislation. I think doing that would be too divisive and risk alienating a significant section of voters.