Constant amount for aviator (5)
I believe the answer is:
pilot
'aviator' is the definition.
(pilot is a kind of aviator)
'constant amount' is the wordplay.
'constant' becomes 'pi' (mathematics: t.l4).
'amount' becomes 'lot' (lot is a kind of amount).
'pi'+'lot'='PILOT'
'for' acts as a link.
(Other definitions for pilot that I've seen before include "-- Whale; -- light" , "Steer, test (scheme)" , "One licensed to fly" , "experimental programme" , "who shows the way?" .)