Conductor's chosen stick, eager to start (9)
I believe the answer is:
electrode
'conductor's' is the definition.
(electrode is a kind of conductor)
'chosen stick eager to start' is the wordplay.
'chosen' becomes 'elect' ('elect' as an adjective can mean chosen).
'stick' becomes 'rod' (I've seen this before).
'to start' indicates taking the first letters.
The first letter of 'eager' is 'e'.
'elect'+'rod'+'e'='ELECTRODE'
(Other definitions for electrode that I've seen before include "Conductor by which current enters" , "Conductor for electricity as it enters or leaves" , "Terminal of, eg, an acid battery" , "Conductor making contact in a circuit" , "Conducting point by which electric current enters or leaves" .)