Eat out, and the rest have to start (4)
I believe the answer is:
etch
'eat out' is the definition.
(thesaurus)
'and the rest have to start' is the wordplay.
'and the rest' becomes 'etc' (et cetera).
'to start' indicates taking the first letters.
The initial letter of 'have' is 'h'.
'etc'+'h'='ETCH'
(Other definitions for etch that I've seen before include "Make a deep impression" , "Use acid to design on metal or glass" , "Inscribe" , "Engrave (metal/glass)" , "Carve into surface of something" .)