Started engine and heard a continuous buzzing sound coming from glove compartment side of car

We would need to look at the car to answer that

It's probably the ABS (Anti-lock Braking System) pump making the noise. You should not hear it running unless your in a hard ABS stop with the tires sliding. You can confirm this is the noise by making a stop that makes the ABS activate and listen to see if it is the same noise. An area with loose gravel on the road works good, so you don't have make such a harsh stop. This will only work while the ABS warning lamp is OFF. If the ABS lamp is on the ABS computer has detected a problem and it prevents the ABS system from functioning altogether. The ABS system stores brake fluid under high pressure to be used for ABS/panic stops. The pump running when it shouldn't is an indication it has a hydraulic leak or a pressure switch that is faulty and it makes the system "think" the pump should run to build back up the brake fluid pressure. If you need help solving this problem please feel free to give Scot or myself a call at 972-420-6187