Lively, not starting to snoop (3)
I believe the answer is:
pry
'snoop' is the definition.
(thesaurus)
'lively not starting' is the wordplay.
'lively' becomes 'spry' (I've seen this before).
'not starting' means to remove the first letter.
'spry' with its initial letter taken away is 'PRY'.
'to' is the link.
(Other definitions for pry that I've seen before include "Be nosey" , "Snoop, poke about" , "Snoop or lever" , "Stick one's nose in" , "Intrusively enquire" .)