Expressions (phrases, clauses, etc.), Godan verb with 'ku' ending
to settle (a problem); to put an end to (a dispute); to be disposed of; to be settled; to come to an end
see 片付く
その論争は完全に片が付いた。That dispute has been settled once and for all.
Also written 方が付く【かたがつく】、片がつく【かたがつく】、方がつく【かたがつく】