The pressure relief valve started leaking on our water heater after seven years. I replaced the valve but it is still leaking. Is there another problem with the water heater or do I need to get a new one?

Problem is most likely with the Pressure Regulating Valve on the water supply. You need to measure the water pressure at the HW heater, it should not exceed 70#.

Actually, code in almost all of the united states says it shall not exceed 80psi.