There's rising hostility in this quarrel (5)
I believe the answer is:
brawl
'this quarrel' is the definition.
(I have seen 'Noisy quarrel ' mean 'brawl' so perhaps 'quarrel' could also mean 'brawl')
'there's rising hostility in' is the wordplay.
'there's' becomes 'bl' (I can't justify this - if you can you should believe this answer much more).
'rising' is a reversal indicator (letters written upwards in a down clue).
'hostility' becomes 'war' (war is a kind of hostility).
'in' indicates putting letters inside.
'war' in reverse letter order is 'raw'.
'bl' going around 'raw' is 'BRAWL'.
Can you help me to learn more?
(Other definitions for brawl that I've seen before include "Abounding" , "Affray" , "Rowdy fight" , "dispute" , "I'd punt for a learned person" .)