Unresponsive having swallowed cold coffee (5)
I believe the answer is:
decaf
'coffee' is the definition.
(type of coffee)
'unresponsive having swallowed cold' is the wordplay.
'unresponsive' becomes 'deaf' (I can't explain this - if you can you should give a lot more credence to this answer).
'having swallowed' is an insertion indicator.
'cold' becomes 'c' (eg on taps).
'deaf' placed around 'c' is 'DECAF'.
Can you help me to learn more?
(Other definitions for decaf that I've seen before include "Style of coffee" , "Less stimulating coffee?" , "Type of coffee" , "Non-alcoholic drink" , "Cup substitute missing kick" .)