To smooth things over, one gets a chap dismissed (4,3)
I believe the answer is:
iron out
'to smooth' is the definition.
(I've seen this in another clue)
'over one gets a chap dismissed' is the wordplay.
'over one' becomes 'i' (Roman numeral. I am not sure about the 'over' bit.).
'gets' means one lot of letters go next to another.
'a chap' becomes 'ron' (short for Ronald).
'dismissed' becomes 'out' (dismissed in cricket).
'i'+'ron'+'out'='IRON OUT'
'things' acts as a link.
Can you help me to learn more?
(Other definitions for iron out that I've seen before include "Settle, put right" , "Resolve" , "Get sorted" , "ready for an evening exercise?" , "Solve (one's differences?)" .)