From Longman Dictionary of Contemporary Englishgive somebody the elbowgive somebody the elbowBritish English informalLEAVE A JOB OR ORGANIZATIONLEAVE A PLACE to tell someone that you no longer like them or want them to work for you and that they should leave → elbow
Examples from the Corpus
give somebody the elbow• The girl must have given him the elbow, Harriet decided.• I won't have anything more to do with you lot till you give him the elbow. 