Director-general's boxing record — admit it's exhausting (9)
I believe the answer is:
depleting
'exhausting' is the definition.
('deplete' can be a synonym of 'exhaust')
'director-general's boxing record admit' is the wordplay.
'director-general' becomes 'DG' (common abbreviation).
'boxing' indicates putting letters inside ('box' can mean contain, as in to put in a box).
'record' becomes 'EP' (abbreviation for extended play record).
'admit' becomes 'let in' (synonyms).
'ep'+'letin'='epletin'
'dg' going around 'epletin' is 'DEPLETING'.
'it's' is the link.
(Another definition for depleting that I've seen is " Using up".)