From Longman Dictionary of Contemporary Englishkeep on the right side of somebodykeep on the right side of somebodyto be careful not to annoy someone, because you want them to help you and not cause problems for you We tried to keep on the right side of the housekeeper, so that she would let us bring beer in. → side
Examples from the Corpus
keep on the right side of somebody• But those wanting to keep on the right side of the law will have to steer clear of the grape.• They were keeping on the right side of the powers that be. 