Cook taking breather round middle of afternoon (5)
I believe the answer is:
grill
'cook' is the definition.
(grilling is a form of cooking)
'breather round middle of afternoon' is the wordplay.
'breather' becomes 'gill' (I've seen this in other clues).
'round' is an insertion indicator.
'middle of' indicates the central letters.
The central letter of 'afternoon' is 'r'.
'gill' going around 'r' is 'GRILL'.
'taking' is the link.
(Other definitions for grill that I've seen before include "Intensely question; dish" , "Question; cook" , "Means of cooking" , "keep on with questions?" , "Screen" .)