Month carrying council leader on staff (7)
I believe the answer is:
sceptre
'staff' is the definition.
(I know that sceptre is a staff)
'month carrying council leader on' is the wordplay.
'month' becomes 'sept' (Sept is an example).
'carrying' indicates putting letters inside.
'leader' suggests taking the first letters.
'on' becomes 're' ('on' can be mean 'with reference to').
The first letter of 'council' is 'c'.
'sept' going around 'c' is 'scept'.
'scept'+'re'='SCEPTRE'
(Other definitions for sceptre that I've seen before include "Royal baton" , "Monarch's ceremonial staff" , "Official staff" , "Rod of office" , "Royal staff (paired with 2 down)" .)