Thanks Jessica! If my VS offer does states I can't do the vac scheme with a TC offer, is it best to just withdraw or worth asking the firm I got the TC from whether I would be able to extend the deadline for signing my contract.
For clarity, it will only be if you have accepted an offer that such a term will be in place. You can hold an offer that you haven't decided on.
If you would not accept a TC with the VS firm over the existing TC offer you have, then I would withdraw from the vacation scheme - there is little to no point doing a vacation scheme if you are definitely going to accept the TC offer you have. If you want to explore the opportunity with the VS firm and may potentially decline/renege the offer with the original TC firm, then you could ask the TC firm to potentially extend the offer period. However, they could decline this request.
Ultimately some people do accept offers, keep it exceptionally quiet (e.g. no posts on social media/don't tell many people) and then continue with the VS despite having accepted a TC elsewhere. Although they will be in breach of their employment contract, they manage to keep it quiet and the VS firm does not always find out. It isn't without its complications though, especially when asked by your VS firm how your other applications/VS opportunities have gone, whether informally during a scheme or during a TC conversion process.
However, I have heard of at least three people this cycle who have had their VS offer withdrawn within this cycle when the firm found out they had an accepted TC offer elsewhere. Ultimately you are in breach of the employment contract, so the firm doesn't have to do anything as such - you have technically terminated the contracted by being in breach of it, rather than the firm having to withdraw the offer.
In this instance, because the term is in the VS offer, not the TC, that is a risk you would take. I think its trickier to consider when the term is in your TC offer though.