"To serve the senator" means to fulfill the needs and carry out tasks for the senator in order to assist them and make their job easier. Full definition
The majority whip is outranked by the majority leader and, unofficially, the president pro tempore; because the office of president pro tempore is largely honorific and usually given to the longest - serving senator of the majority, the majority whip is in reality the second - ranking senator in the majority conference in terms of actual power. (en.wikipedia.org)
Johnson served an astonishing 20 terms in the New York State Senate and is believed to be the second longest serving senator in the chamber's history. (thealbanyproject.kinja.com)
Amedore lost the recount by 18 votes giving him the honor of being NY State's shortest serving Senator at that time. (nystateofpolitics.com)