This card is an identical reprint of the House, Stats, Icons and abilities of the Iron Thrones rare but uses the Art of the Five Kings Edition Uncommon Brienne.

Is it legal to use the Iron Thrones Edition Brienne with identical gameplay but different art?

Yes. As long as all stats, traits, keywords, crests, icons, and text is identical two cards of the same name are considered to be the same, even if the art is not.