Slight problem with award after chick goes naked (6)
I believe the answer is:
hiccup
'slight problem' is the definition.
'award after chick goes naked' is the wordplay.
'award' becomes 'cup' (I've seen this in other clues).
'after' is a charade indicator (letters next to each other).
'goes naked' indicates the central letters (the outside letters are removed).
The centre of 'chick' is 'hic'.
'cup' after 'hic' is 'HICCUP'.
'with' is the link.
(Other definitions for hiccup that I've seen before include "Minor problem" , "Involuntary spasm of the diaphragm" , "Sudden throat sound or minor mishap" , "Involuntary glottal closure" , "Reflex spasm of the diaphragm" .)