I'm installing a new heat pump and coils, my contractor sais I don't need to install a new air handler, is true that it will be OK?

You don't have to get a new air handler, as long as they can make the new coil fit into the old air handler. I would advise replacing the air handler as well, only a couple hundred bucks more, and you know you have all new parts, and nothing to worry about for awhile.