Can I still apply a visa if my student visa runs out in 3 days?

I am on a student visa due to some litigations with partner was late to apply for extended visa. Just left with 3days. Can I still apply for another visa in this 3days?

Yes, as long as you submit your application and pay for it within 3 days then it should be all OK.
Btw, which visa are you planning to apply?

Indefinite leave to remain or a student visa for a different course again.

You have to be careful here.

If you apply for a visa, it has to be a correct and valid application. If your application is rejected or refused, that's it. You won't be able to lodge further applications in the UK.

On which basis do you want to lodge an ILR application?

For how many years have you been a student. Some immigration history would help here.

And I would expect that you would have also had to of already been provisionally accepted onto a recognised course (as opposed to one of the fake ones we have been hearing about) to be able to apply for a student visa.

How will you support yourself, is probably a question that will need answering?