Can it be successful to apply for a new student ID card after canceling the Singapore student ID card for more than 3 months?

You may be refused a visa. It's best to make it clear with the current school.

The possible situations are as follows:

(1) The school reported your information to the Immigration Bureau, so it is impossible for you to get a visa again;

(2) The school did not report your information to the Immigration Bureau. There seems to be nothing wrong. In fact, your information is recorded in the immigration department. If your name is found and you are still in your previous school, it is estimated that you will not get a visa.

(3) Immigration has no record of you, no problem.