Little hesitation about the time — very keen (5)
I believe the answer is:
eager
'very keen' is the definition.
(I've seen this before)
'little hesitation about the time' is the wordplay.
'little hesitation' becomes 'er'.
'about' is an insertion indicator.
'the time' becomes 'age' (age is a kind of time).
'er' placed around 'age' is 'EAGER'.
(Other definitions for eager that I've seen before include "Excited by desire" , "Like some beavers" , "Enthusiastic, agog" , "Keen (as a beaver?)" , "Alert and active type?" .)