hard to start after driven or a hot engine. have installed new fuel pump on 1993 Chevrolet Corvette

when the engines cold if fires on the first turn

Asked by for the 1993 Chevrolet Corvette
did you replace fuel filter also
yes it has a new filter also, when its cold its a first crank start
1 more answer
I suggest you check the electrical resistance of the fuel injectors. Check cold then check again hot. Shorted fuel injector winding[s] can cause this symptom. The resistance readings will change with temp. however the individual injector resistances should all be the same or close to the same.