Realistically, no.
Usually you retire after a 30 year career. Assuming he was flying F14's in his mid-20's, he wouldn't still be in the Navy at 60.
However we don't know how much time has elapsed between the end of the 1st movie and this one.
We know that Iceman made Admiral, and he specifically requested Maverick to be read in for this mission. Assuming that they were close in age, they must both be close to the end of their careers.
Of course Maverick being Maverick, I'm surprised that he lasted close to 30 years without getting tossed out for buzzing the tower or making high speed passes over some admiral's daughter/granddaughter.