The impetus for Marcus taking the sergeants exam is the pay increase, however he doesn't need stop being a detective in order to get a pay increase. Since Marcus says that he will get an increase if he makes sergeant, it can be assumed that he is only a detective 3rd grade
In the NYPD a detective 2nd grade get paid as much as a sergeant, while a detective 1st grade gets the pay of a lieutenant.
Detectives are promoted based on their performance, so Marcus should have been able to get a promotion just by asking for one.