Noel Coward wrote this complaint (3,5)
I believe the answer is:
hay fever
'noel coward wrote this complaint' is the definition.
'hay fever' can be an answer for 'complaint' (medical complaint). I am not sure about the remainder of the definition.
'wrote this complaint' is the wordplay.
'wrote' becomes 'hay' (I can't explain this - if you can you should give a lot more credence to this answer).
'this complaint' becomes 'fever'.
'hay'+'fever'='HAY-FEVER'
(Other definitions for hay fever that I've seen before include "Coward created this" , "Allergy with asthmatic symptoms caused by pollen or dust" , "Allergy caused by pollen, dust etc" , "summer glums?" , "Seasonal rhinitis" .)