Secure promotion in C branch (5)
I believe the answer is:
climb
'secure promotion' is the definition.
(as in climbing the ranks)
'c branch' is the wordplay.
'branch' becomes 'limb' (I've seen this before).
'c'+'limb'='CLIMB'
'in' acts as a link.
(Other definitions for climb that I've seen before include "Go higher up" , "Get higher" , "Rise to a higher level" , "Go up - scale" , "Scale or clamber" .)