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Brooks Orpik playing for Washington Capitals won Stanley Cup in 2009 with Pittsburgh Penguins.

Vegas goaltender Marc-André Fleury has thee Stanley Cups - similar with Penguins - in 2009, 2016 and 2017.

Both Orpik and Fleury also played in 2008, where Penguins lost to Detroit Red Wings.

In the 2017 Stanley Cup Finals James Neal played for Nashville Predators, Predators lost the series to Penguins 2-4. He also currently plays for Vegas Golden Knights.

This should be all players with previous Stanley Cup final appearances from the rosters of the the two finalists according to sources below and also according to the Wikipedia article 2018 Stanley Cup Finals. (Here is link to the current revision. Notice the column "Finals appearance" in the section Team rosters.)