Chilled Italian monk with no love for his boss? (6)
I believe the answer is:
frappe
'chilled' is the definition.
(I've seen this before)
'italian monk with no love for his boss?' is the wordplay.
I cannot really see how this works, but
'monk' could be 'fra' (I have seen 'Italian monk ' mean 'fra' so perhaps 'monk' could also mean 'fra') and 'fra' is found within the answer.
This explanation may well be incorrect...
(Other definitions for frappe that I've seen before include "Like a cold drink" , "served cold" , "booze" , "Fruit drink frozen to a mush" , "Of a drink, served iced or chilled" .)