Lead Civil Engineer, after promotion, getting rise (7)
I believe the answer is:
advance
'rise' is the definition.
(advancing is a kind of rising)
'lead civil engineer after promotion' is the wordplay.
'lead' becomes 'van' (van is the leading part of a movement or group).
'civil engineer' becomes 'ce'.
'after' says to put letters next to each other.
'promotion' becomes 'ad' (short for advert).
'van'+'ce'='vance'
'vance' put after 'ad' is 'ADVANCE'.
'getting' is the link.
(Other definitions for advance that I've seen before include "Move forward like army or loan against wage" , "Move forward to get loan?" , "Make headway" , "Loan; promotion" , "Put forward (a theory)" .)