Hold out the olive branch is a common phrase that means to make peace or end conflict with someone. However, there are a few other phrases that also convey this same idea. One of them is "bury the hatchet," which means to forgive past offenses and start anew. Another synonym is "extend an olive branch," which is a bit more formal than the first two. "Turn the other cheek" is another phrase that conveys a similar idea, suggesting that one should ignore offenses rather than retaliate. Finally, "make amends" is another good synonym for "hold out the olive branch," implying that one party wants to reconcile and end any bad blood between them.