Briefly pass around gossip, enthusiastically at first, to canvass opinion (3,1,4)
I believe the answer is:
fly a kite
'canvass opinion' is the definition.
(fly a kite can mean to test public opinion)
'briefly pass around gossip enthusiastically at first' is the wordplay.
'briefly pass' becomes 'flit' (to flit around is to move quickly).
'around' is an insertion indicator.
'gossip' becomes 'yak'.
'at first' suggests taking the first letters.
The first letter of 'enthusiastically' is 'e'.
'flit' placed around 'yak' is 'flyakit'.
'flyakit'+'e'='FLY A KITE'
'to' acts as a link.
(Other definitions for fly a kite that I've seen before include "Pilot" , "Test opinion by circulating rumours" , "What co-pilots do" , "Release information to test public opinion" .)