'Old Tony' is one of Mary Seymour’s lovers (see Episode 4 and Episode 6) whose wife had passed away. He is referred to as ‘old’ to distinguish him from ‘Young Tony’ another of Mary’s lovers. This leads to the inevitable joke about Mary's two-toned hair.
Old Tony once 'bested' Young Tony in a physical altercation.
In Episode 39 we hear that Old Tony had sadly passed away.