Great admirer I finish with in due course (8)
I believe the answer is:
idolater
'great admirer' is the definition.
(I've seen this before)
'i finish with in due course' is the wordplay.
'finish' becomes 'do'.
'with' is a charade indicator (letters next to each other).
'in due course' becomes 'later' (I've seen this before).
'i'+'do'+'later'='IDOLATER'
(Other definitions for idolater that I've seen before include "Strong admirer" , "great admirer" , "devoted fan" , "Huge admirer" , "One admires" .)