Conciliatory gesture made by Oscar, as it happens, with backing of department (5,6)
I believe the answer is:
olive branch
'conciliatory gesture' is the definition.
(I've seen this before)
'oscar as it happens with backing of department' is the wordplay.
'oscar' becomes 'O' (phonetic alphabet: alpha, bravo, charlie etc.).
'as it happens' becomes 'live' (as in live television).
'with' means one lot of letters go next to another.
'backing of department' becomes 'branch' (I can't justify this - if you can you should believe this answer much more).
'o'+'live'+'branch'='OLIVE BRANCH'
'made by' is the link.
Can you help me to learn more?
(Other definitions for olive branch that I've seen before include "Symbol of peace" , "One offered in peace" , "attempt at conciliation" , "Peace gesture" , "conciliatory gesture" .)