Existing visa expires when new visa application ongoing

These kind of questions are answered in multiple times. You should read older threads to get the answer.

Your EP application is a separate process, it has no link to your visa. If your pass is expiring in two weeks time then you should plan to leave the country on or before to the expiring date. You must have to wait the outcome of the EP application before you could think of entering the country.

Try to avoid overstaying and also avoid visa run (that means go to a neighbour country for a week then try to enter Singapore again hoping to get another 30 days visa). For any further questions, try to go through older threads as most of the queries we have answered multiple times. Good luck

You can ask ICA for an extension of the SVP, by submitting proof of the EP application.
They may or may not allow you to stay until the EP is issued. If not, you must leave the country.

@beppi, Just to clarify I mean I am on STP(Student Pass) and have been told to surrender upon conferment from the university.

I have now learned that I will be automatically given an SVP upon surrender of STP which is valid for 89 days and if needed beyond that I can apply for LTVP. Is that correct?

If you get the SVP, then you can do as I wrote above at the end of its validity.