Dessert on infirm chapel beam (5,5)
I believe the answer is:
peach melba
'dessert' is the definition.
'infirm chapel beam' is the wordplay.
'infirm' indicates an anagram.
'chapel'+'beam'='chapelbeam'
'chapelbeam' is an anagram of 'PEACH MELBA'.
'on' is the link.
(Other definitions for peach melba that I've seen before include "Dame Nellie's dish" , "Sweet" , "fruity dessert" , "Ice cream dish with fruit" .)