When my heat pump comes on the circuit breaker panel buzzes. It is on a separate breaker. Please tell me what I need to do. Thank you

Most likely the most needed to be done will be to replace the breaker with a new one of the same amp rating. The contacts and/or the thermal magnetic components may be weakened.

But be sure to inspect the busbar the breaker plugs onto carefully to be sure there is no discoloration or melting of the metal due to a loose connection that may have caused heat.