Do I need a diaphram tank when I'm on city water now

If by diaphram tank you mean a bladder tank, which is a type of storage tank on a well system, the answer is no. However, a small expansion tank is used in conjunction with a water heater when a check valve is installed to prevent heat loss back up the cold water line.

Does your water heater T & P valve drip? Do you have a sprinkler system ?Let me know, Tom