Mum's right in with the war-god (4)
I believe the answer is:
mars
'god' is the definition.
(Mars is an example)
'mum's right in' is the wordplay.
'mum's' becomes 'ma's' (ma can mean mother).
'right' becomes 'r' (common abbreviation).
'in' means one lot of letters goes inside another.
'mas' going around 'r' is 'MARS'.
'with the war' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for mars that I've seen before include "March to the French" , "Next planet out" , "Fourth planet from the Sun" , "Possibly pollutes" , "one associated with war" .)