Beginning to coach more promising staff (7)
I believe the answer is:
crosier
'staff' is the definition.
(crosier is a kind of staff)
'beginning to coach more promising' is the wordplay.
'beginning to' says to take the initial letters.
'more promising' becomes 'rosier' ('rosy' can be a synonym of 'promising').
The first letter of 'coach' is 'c'.
'c'+'rosier'='CROSIER'
(Other definitions for crosier that I've seen before include "A bishop's staff as symbol of office" , "Ecclesiastical staff" , "Staff carried by a bishop" , "Bishop's crook" , "one's hooked!" .)