Girl at home suffered back cramps (5)
I believe the answer is:
dinah
'girl' is the definition.
'home suffered back cramps' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'suffered' becomes 'had' (have can mean to undergo or suffer).
'back' is a reversal indicator.
'cramps' is an insertion indicator (inserted letters are cramped or obstructed).
'had' back-to-front is 'dah'.
'in' going within 'dah' is 'DINAH'.
'at' is the link.
(Other definitions for dinah that I've seen before include "Washington perhaps" , "_____ 15+22, singer" .)