The Hull-based company has operated a telephone system, independent from BT, for the city's residents over more than a century.
The winning agency will primarily promote Affiniti, Kingston's business arm that offers fixed-line and mobile telecoms, data storage and security to firms. It has expanded its offering from its East Yorkshire base, with coverage now available from Plymouth to Edinburgh.
The company has strengthened the Affiniti operation over the past couple of years with the purchases of Omnetica, for £169m, and Technica UK, for £3.5m.
Three-year incumbent agency Kaizo is one of four invited to pitch for the account. The shortlist will be whittled down to two agencies ahead of an appointment in May.
Kingston said it needed to review its B2B support as the business expanded.
The firm made headlines recently following a failed approach from US private equity group Carlyle. The companies could not agree on structure or price, triggering a slump in Kingston's share value last week when the bid was finally rejected.
Kingston Interactive Television, the country's first broadband TV service, was wound up this month due to lack of subscribers.
The winning agency will report to Kingston director of comms Anita Pace, working alongside financial comms agency Maitland.