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A representative of the clan, Varrin Axebreaker, wishes to hire the characters to learn how to access the treasure.", and "Varrin Axebreaker (lawful good, dwarf noble)" and "My name is Varrin Axebreaker, and I have a proposition for you. My clan has located wealth stolen from us many years ago, but it’s sealed in a vault that’s magically locked. If you can recover the key—whatever it is—you’ll gain the undying gratitude of Clan Axebreaker."
He's a representative of a clan who is a noble bearing the name of the clan and who has the authority to grant clan wealth and gratitude. He works for that government.
There is no Axebreaker clan associated with Mithril Hall. That clan was Battlehammer.
"Revel’s End is controlled by the Lords’ Alliance, a loose confederation of settlements whose current members include the cities of Baldur’s Gate, Mirabar, Neverwinter, Silverymoon, Waterdeep, and Yartar; the towns of Amphail, Daggerford, and Longsaddle; and the dwarven stronghold of Mithral Hall."
The Lords' Alliance includes those named there, but also others. The FR wiki has an incomplete list of 15 members. The adventure says "All 10" for members, but there are more than 10. Chalk that one up to poor research and/or "there's no such thing as canon."
If Clan Axebreaker is using that prison, they would also be part of the Lords' Alliance.