What NFL player holds the record for playing the most seasons in the league AFTER their first Super Bowl appearance?

Adam Vinatieri. He played in the Super Bowl with New England at the end of his rookie season of 1996, and he then ran up the third-longest career in history (24 years, retiring in 2019). Thus, he played 23 years in the NFL after his first Super Bowl appearance. The only two players with as-long or longer careers were George Blanda (26 years starting in 1949, but the Super Bowl didn't begin until 1966) and Morten Andersen (25 years starting in 1982, but he didn't make his first Super Bowl until 1998). Tom Brady, who just retired after 22 seasons, made his first Super Bowl at the end of his second season, so (assuming he stays retired) his streak was only 20 years.
https://apsportseditors.org/nfl/average-nfl-career
https://en.wikipedia.org/wiki/Adam_Vinatieri