His or her successor is on time (5)
I believe the answer is:
their
'his or her' is the definition.
(I've seen this before)
'successor is on time' is the wordplay.
'successor' becomes 'heir' (synonyms).
'is on' means one lot of letters go next to another.
'time' becomes 't' (abbreviation).
'heir' put after 't' is 'THEIR'.
(Other definitions for their that I've seen before include "Some would say his (or her)" , "Belonging to those people" , "Possessive pronoun" , "Those people's" , "Relating to them" .)