By “heat pump” I assume you mean a hot water circulation pump in a zoned hot water heating system. Such pumps use centrifugal impellers to pump water through the system. They should not need to be “primed” but the system must be full of water for them to work.
Make sure that the system is indeed full of water and any air has been bled from it. Make sure that the thermostatically controlled zone valve is open. If the system is full of water and the pump operates as you describe, then you either have a stuck zone valve or there is something wrong at the pump, such as a worn, broken, or disconnected impeller.
In multizone hot water systems there are two basic setups: 1) a single circulation pump feeding a manifold that distributes hot water through two or more zone valves; and, 2) a system where there is a separate pump for each zone, with the thermostats activating the pumps when heat is demanded. I’ve installed both systems. The first is cheaper and easier to install. I prefer the second as being more reliable and durable in the long run.