His or her successor supports bequest, in the end (5)
I believe the answer is:
their
'his or her' is the definition.
(I've seen this before)
'successor supports bequest in the end' is the wordplay.
'successor' becomes 'heir' ('heir' can be a synonym of 'successor').
'supports' is a charade indicator (letters next to each other) (bottom letters provide a support for the top ones).
'in the end' indicates one should take the final letters.
The last letter of 'bequest' is 't'.
'heir' after 't' is 'THEIR'.
(Other definitions for their that I've seen before include "Belonging to him (perhaps wrongly)" , "belonging to an individual" , "Possessive pronoun" , "Belonging to those people" , "Relating to them" .)