Cook fish part holding skewer's end (5)
I believe the answer is:
grill
'cook' is the definition.
(grilling is a form of cooking)
'fish part holding skewer's end' is the wordplay.
'fish part' becomes 'gill' (I've seen this in another clue).
'holding' is an insertion indicator.
'end' says to take the final letters.
The last letter of 'skewer' is 'r'.
'gill' going around 'r' is 'GRILL'.
(Other definitions for grill that I've seen before include "Cook under direct heat" , "keep on with questions?" , "what restaurant has to offer?" , "Question closely" , "Question hard" .)