The phrase "party whip" refers to a role in politics where a designated person ensures that members of a political party vote in line with the party's decisions and policies. They help maintain party discipline and unity. Full definition
Ballard became the election agent for A. V. Alexander in the Sheffield Hillsborough constituency in 1922; [1] Alexander gained the seat for the Co-operative Party, taking the Labour Party whip in Parliament. (en.wikipedia.org)
Then there are peers with hereditary titles, where succeeding generations take a different party whip from their forebears. (theconversation.com)
Mercer resigned the Conservative Party whip on 31 May 2013 after an investigation by the Daily Telegraph and BBC's Panorama caught him on camera accepting payment for lobbying. (en.wikipedia.org)