It's constant for each musician (5)
I believe the answer is:
piper
'musician' is the definition.
(someone playing the bagpipes)
'it's constant for each' is the wordplay.
'it's constant' becomes 'pi' (mathematics: 3.14).
'for each' becomes 'per' (per person).
'pi'+'per'='PIPER'
(Other definitions for piper that I've seen before include "If you pay him, call the tune" , "'Liam O'Flynn or Seamus Ennis, say (5)'" , "Instrumentalist, solo or military" , "Musician (who gets paid?)" , "English painter and stained glass designer, d. 1992" .)