Those people taking subject, not finishing (4)
I believe the answer is:
them
'those people' is the definition.
(I've seen this before)
'subject not finishing' is the wordplay.
'subject' becomes 'thema' (I have seen 'Latin subject' mean 'thema' so perhaps 'subject' could also mean 'thema').
'not finishing' means to remove the last letter.
'thema' with its final letter taken away is 'THEM'.
'taking' is the link.
(Other definitions for them that I've seen before include "Others" , "... in another case, they" , "Those people (as object)" , "Perhaps, the Opposition" , "Let -- eat cake" .)