Which pulley? delflection? idler tensioner?
Have you checked all other pulleys? AC, steering pump, etc? Also the Alternator.
You can check by releasing tension and freeing the belt and spinning the pulleys ( with engine off of course) and if it spins freely and is rattly then it needs changing.
Alterntively turn on engine and place a large screwdrive next to the pulley and the noise will be amplified when you place your ear closest.
Failing all the above. Start to look and fan couplings, heat shields, exhaust mounts or possible clutch release bearing.
All the best