To extend an offer or gesture of peace, reconciliation, truce, etc. (to someone), so as to end a disagreement or dispute. (Can also be formulated as "offer someone the olive branch.") If you find yourself in a spat with a friend, try to be the bigger person and be the one to offer the olive branch. I was still hurt by the way my parents had lied to me, but I decided to offer them the olive branch at Christmas.