Father accepting story in leaflet (5)
I believe the answer is:
flier
'leaflet' is the definition.
(I've seen this before)
'father accepting story' is the wordplay.
'father' becomes 'fr' (abbreviation as in a priest's title).
'accepting' means one lot of letters goes inside another (inserted letters are accepted).
'story' becomes 'lie' (story can mean a fabrication).
'fr' going around 'lie' is 'FLIER'.
'in' acts as a link.
(Other definitions for flier that I've seen before include "Rifle for airman" , "Risk" , "Circular" , "PO, for example" , "Aviator" .)