Staff beginning to miss service (4)
I believe the answer is:
mace
'staff' is the definition.
(mace is a kind of staff)
'beginning to miss service' is the wordplay.
'beginning to' suggests taking the first letters.
'service' becomes 'ace' (ace is a kind of service**).
The first letter of 'miss' is 'm'.
'm'+'ace'='MACE'
(Other definitions for mace that I've seen before include "Came to get ancient weapon" , "put on the rack?" , "Came to get ceremonial staff" , "Ceremonial staff or kind of spice" , "Spice; ceremonial baton" .)