Right line taken in winning point of quarrel (9)
I believe the answer is:
arrowhead
'point of quarrel' is the definition.
(quarrel is a type of arrow)
'right line taken in winning' is the wordplay.
'right' becomes 'r' (common abbreviation).
'line' becomes 'row' (row is a kind of line**).
'taken in' means one lot of letters goes inside another.
'winning' becomes 'ahead' (I've seen this before).
'r'+'row'='rrow'
'rrow' inserted inside 'ahead' is 'ARROWHEAD'.
(Other definitions for arrowhead that I've seen before include "Tip of an old projectile" , "Point to a weapon" , "A suitable end for weapon" , "Water plant" .)