Runaway has pudding with no small hesitation (8)
I believe the answer is:
deserter
'runaway' is the definition.
(I've seen this in another clue)
'pudding with no small hesitation' is the wordplay.
I cannot really see how this works, but
'small' could be 's' (abbreviation - e.g. clothes size) and 's' is present in the answer.
'hesitation' could be 'er' (sound used when hesitating) and 'er' is located in the answer.
The remaining letters 'deter' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
'has' is the link.
Can you help me to learn more?
(Other definitions for deserter that I've seen before include "Renegade" , "military offender" , "Rat" , "One illegally leaving armed forces" , "Military runaway" .)