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 in reverse.
'following' says to put letters next to each other.
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
'heady'+'offer'='headyoffer'
The alternating letters of 'headyoffer' are 'hayfe'.
'rev' reversed gives 'ver'.
'ver' put 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" .)