Household deity finishes quarrel with a right (3)
I believe the answer is:
lar
'household deity' is the definition.
(I've seen this in another clue)
'finishes quarrel with a right' is the wordplay.
'finishes' indicates one should take the final letters (I've seen 'finish' mean this).
'with' is a charade indicator (letters next to each other).
'a right' becomes 'ar' (I've seen this in other clues).
The last letter of 'quarrel' is 'l'.
'l'+'ar'='LAR'
(Other definitions for lar that I've seen before include "statue of a god" , "Roman household god" , "Libya" , "What's supposed to protect the house" .)