Measure of noise coming from celeb I'd beaten up (7)
I believe the answer is:
decibel
'measure of noise' is the definition.
(unit of loudness)
'celeb i'd beaten up' is the wordplay.
'beaten up' indicates anagramming the letters.
'celeb'+'id'='celebid'
'celebid' with letters rearranged gives 'DECIBEL'.
'coming from' acts as a link.
(Other definitions for decibel that I've seen before include "Unit of volume" , "Noise unit" , "Measure of noise intensity" , "Sound level unit" , "Unit for measuring intensity of sound" .)