Half-hearted, cross staff (3)
I believe the answer is:
rod
'staff' is the definition.
(both can mean a stick or cane)
'half-hearted cross' is the wordplay.
'half' becomes 'first half' (first half is a kind of half).
'hearted' says to take the centre.
'cross' becomes 'od' (I can't justify this - if you can you should believe this answer much more).
The middle of 'first' is 'r'.
'r'+'od'='ROD'
Can you help me to learn more?
(Other definitions for rod that I've seen before include "Baton, pole" , "Fishing implement" , "Long bar or pole" , "- - , pole or perch" , "Fishing pole" .)