Put an end to, then encourage, a snack (6,3)
I believe the answer is:
scotch egg
'a snack' is the definition.
(a Scotch egg might be eaten as a snack)
'put an end to then encourage' is the wordplay.
'put an end' becomes 'scotch' (I've seen this before).
'to then' means one lot of letters go next to another.
'encourage' becomes 'egg'.
'scotch'+'egg'='SCOTCH EGG'
(Other definitions for scotch egg that I've seen before include "It is encased in sausage meat" , "One cased in sausage meat" , "Picnic food" , "Snack made largely of sausage meat" , "Hard-boiled item in sausage meat" .)