Supposedly for the second time completely during a the Super Bowl era (as the Packers have two different teams that did it if you count the pre-Super Bowl era)...
But for the second time completely during the Super Bowl era, a player has completed the three peat and gotten three Super Bowl rings in a row.
OL Darian Kinnard has won a Super Bowl ring with the Eagles, after winning one the last two years with the Chiefs. Though, it should be noted that he has not yet actually played in a Super Bowl, just been bench backup on the teams that won the Super Bowl.
Prior to this, LB Ken Norton Jr. led the Cowboys in tackling for the two years they beat the Bills in the Super Bowl, and Cowboys let him and others leave before the first year of the Salary Cap in 1994, which the 49ers signed him and he got 1st team All-Pro while helping them to another Super Bowl.