If I already have an existing valid Singapore driving licence and had just passed another class of driving licence (eg: Has Class 3A licence and pass my Class 3 Traffic Police Practical test), do I need to apply for the QDL?

No, you do not need to apply for your QDL. 

After you had passed the practical test, the driving tester at the Traffic Police Test Centre will assist to paste an endorsement sticker (with the new class of QDL that you had passed) at the back of your existing valid Singapore photo card driving licence. 

There is no fee charged for the endorsement of your new class of driving licence. 

Please note that if you do not endorse your QDL, you will not be allowed to drive or ride.