The word has a special meaning in British English
British member of Parliament (or MP) Jo Cox was murdered while meeting with citizens in the district she represented, a regular gathering known in Britain as a surgery, which means “a special period of time when people can visit a member of the British Parliament to ask questions.” This kind of meeting is sometimes referred to as an “advice surgery” or a “constituency surgery.”
This definition is entered in Merriam-Webster’s Learner’s Dictionary, which is written for people who are learning English. Traditionally, Merriam-Webster dictionaries have focused on American English, but greater coverage of international varieties of English is important for a learner’s dictionary because of the global interest in English.
This meaning of surgery comes from the British name for a doctor’s office—where a doctor meets with patients—and was extended to mean both “office hours” generally and “time for visiting with constituents” specifically.