Last of kids shut up, being exhausted! (5)
I believe the answer is:
spent
'being exhausted' is the definition.
('spent' can be a synonym of 'exhausted')
'last of kids shut up' is the wordplay.
'last of' indicates one should take the final letters.
'shut up' becomes 'pent' (synonyms).
The last letter of 'kids' is 's'.
's'+'pent'='SPENT'
(Other definitions for spent that I've seen before include "Used up; exhausted" , "Expended" , "Worn Out, exhausted" , "Worn out, having laid out money" , "Splashed out" .)