Going with some hesitation to tender (5)
I believe the answer is:
'to tender' is the definition.
('offer' can be a synonym of 'tender')
'going with some hesitation' is the wordplay.
I cannot really see how this works, but
'going' could be 'off' (I've seen this in another clue) and 'off' is found within the answer.
'hesitation' could be 'er' (sound used when hesitating) and 'er' is found within the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for offer that I've seen before include "killer?" , "Express willingness - present" , "Expression of willingness to pay or give" , "Tender - proposal" , "Make available for sale" .)