Complaint clergyman withdraws following oddly heady offer (3,5)
I believe the answer is:
hay fever
'complaint' is the definition.
(medical complaint)
'clergyman withdraws following oddly heady offer' is the wordplay.
'clergyman' becomes 'rev' (short for reverend).
'withdraws' says the letters should be written backwards.
'following' is a charade indicator (letters next to each other).
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
'heady'+'offer'='headyoffer'
The alternating letters of 'headyoffer' are 'hayfe'.
'rev' backwards is 'ver'.
'ver' after 'hayfe' is 'HAY-FEVER'.
(Other definitions for hay fever that I've seen before include "Seasonal rhinitis" , "summer glums?" , "Allergy - Noel Coward comedy" , "Coward's" , "The result of an allergic reaction to pollen" .)