Begs fashionable models to eat seconds (7)
I believe the answer is:
insists
'begs' is the definition.
(insisting is a kind of begging)
'fashionable models to eat seconds' is the wordplay.
'fashionable' becomes 'in' (in can mean fashionable or trendy).
'models' becomes 'sits' ('sit' can be a synonym of 'model').
'to eat' is an insertion indicator.
'seconds' becomes 's' (abbreviation).
'sits' enclosing 's' is 'sists'.
'in'+'sists'='INSISTS'
(Other definitions for insists that I've seen before include "Demands firmly, not accepting refusal" , "Maintains persistently" , "Contends" , "Maintains firmly" , "Brooks no refusal" .)