Relation dropping a girl for falsehood (7)
I believe the answer is:
untruth
'for falsehood' is the definition.
(synonyms)
'relation dropping a girl' is the wordplay.
'relation' becomes 'aunt' (aunt is a kind of relation).
'dropping' is a deletion indicator.
'girl' becomes 'ruth' (girl's name).
'aunt' with 'a' taken out is 'unt'.
'unt'+'ruth'='UNTRUTH'
(Other definitions for untruth that I've seen before include "story" , "Falsehood or lie" , "A genuinely deniable" , "Fiction" , "product of Orwell's ministry?" .)