Blow up in last half after hours (7)
I believe the answer is:
inflate
'blow up' is the definition.
(synonyms)
'in last half after hours' is the wordplay.
'last' says to take the final letters.
'after hours' becomes 'late' (I've seen this in other clues).
The final letter of 'half' is 'f'.
'in'+'f'+'late'='INFLATE'
(Other definitions for inflate that I've seen before include "Make bigger" , "Exaggerate or fill with air" , "Cause to swell" , "Fill with gas" , "Get air into" .)