Exhausted and insensitive to the rhythm (4,4)
I believe the answer is:
dead beat
'exhausted' is the definition.
(I've seen this before)
'insensitive to the rhythm' is the wordplay.
'insensitive' becomes 'dead' (I've seen this before).
'to the rhythm' becomes 'beat' (synonyms).
'dead'+'beat'='DEAD-BEAT'
'and' is the link.
(Other definitions for dead beat that I've seen before include "An American down-and-out" , "Spent" , "An informal down-and-out" , "Idle, feckless or disreputable person" , "Ready to drop" .)