Bet Anne put out feelers (8)
I believe the answer is:
antennae
'feelers' is the definition.
('antenna' can be a synonym of 'feeler')
'bet anne put out' is the wordplay.
'bet' becomes 'ante' (ante is a kind of bet).
'put out' indicates an anagram.
'anne' with letters rearranged gives 'nnae'.
'ante'+'nnae'='ANTENNAE'
(Other definitions for antennae that I've seen before include "Sensory appendages on insects" , "They'll pick up signals" , "They sense" , "Russian wolfhound" , "Insect's feelers" .)