Apostate finally accepted by respectable relative (5)
I believe the answer is:
niece
'relative' is the definition.
(type of relative)
'apostate finally accepted by respectable' is the wordplay.
'finally' suggests the final letters.
'accepted by' indicates putting letters inside (inserted letters are accepted).
'respectable' becomes 'nice' (similar in meaning).
The last letter of 'apostate' is 'e'.
'e' placed into 'nice' is 'NIECE'.
(Other definitions for niece that I've seen before include "girl further down the line" , "member of different generation" , "Young female relative" , "Family girl" , "Brother's girl" .)