From Longman Dictionary of Contemporary Englishbe on your best behaviourbe on your best behaviourPOLITEto behave as well and politely as you can in order to please someone I want you both to be on your best behaviour at Grandad’s. → behaviour
Examples from the Corpus
be on your best behaviour• Dinner was very formal, with everyone on their best behaviour.• And if what Cadfael suspected was indeed true, he had now good reason to be on his best behaviour.• But everyone is on their best behaviour.• So when we arrived hopefully at Loch Hope that morning, I was on my best behaviour.• Use only our own girls and warn them to be on their best behaviour. 