allow to remain in a place or position; "We cannot continue several servants any longer"; "She retains a lawyer"; "The family's fortune waned and they could not keep their household staff"; "Our grant has run out and we cannot keep you on"; "We kept the work going as long as we could"
If you keep someone on, you continue to employ them, for example after they are old enough to retire or after other employees have lost their jobs. Sometimes they keep you on a bit longer if there's no one quite ready to step into your shoes