By 2269, he was 125 years old. Though still vital, Captain James T. Kirk thought that he looked twice his age. He had also recently celebrated his seventh decade in service and was considered something of a Starfleet institution. (TOS novel: Allegiance in Exile)
It is not certain that Walkowski was a 'four star' Admiral. However, it is likely that his rank was of a senior grade given his stated time in service.