Coppers' old boss and one less senior creak at the edges (4)
I believe the answer is:
dick
'coppers' old boss' is the definition.
(Cressida Dick, former Met Police Commissioner)
'one less senior creak at the edges' is the wordplay.
'one less senior' becomes 'di' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'at the edges' suggests removing the centre.
'creak' with its middle taken out is 'ck'.
'di'+'ck'='DICK'
'and' is the link.
(Other definitions for dick that I've seen before include "-- Turpin" , "may be spotted eating" , "See 7" , "-- Van Dyke, actor" , "See 20 Across" .)