Chief holy man is after a Christmas tree (5)
I believe the answer is:
first
'chief' is the definition.
(I've seen this in another clue)
'holy man is after a christmas tree' is the wordplay.
'holy man' becomes 'st' (abbreviation for saint).
'is after' says to put letters next to each other.
'a christmas tree' becomes 'fir' (firs are often used as Christmas trees).
'st' after 'fir' is 'FIRST'.
(Other definitions for first that I've seen before include "to begin with" , "Top degree class" , "Prime" , ""Eclipse _____ ..." , "Preceding all others" .)