… and writer that's exhausted (5)
I believe the answer is:
spent
'exhausted' is the definition.
(I know that exhausted can be written as spent)
'and writer' is the wordplay.
I cannot quite see how this works, but
'and' could be 'n' (common abbreviation for 'and') and 'n' is present in the answer.
The remaining letters 'spet' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
'that's' acts as a link.
(Other definitions for spent that I've seen before include "Burned-out" , "Paid out - finished" , "Expended" , "Worn Out, exhausted" , "Used up; exhausted" .)