Finish off officer classes (6)
I believe the answer is:
genera
'classes' is the definition.
(I've seen this before)
'finish off officer' is the wordplay.
'finish off' means to remove the last letter.
'officer' becomes 'general' (general is a kind of officer).
'general' with its last letter taken away is 'GENERA'.
(Other definitions for genera that I've seen before include "Groups between family and species (biology)" , "similar groups" , "Groups with common characteristics" , "Taxonomic categories (biology)" , "Biological groupings" .)