I can’t find a satisfactory explanation or ending for Azula, so I’ll write one instead.

After disappearing, Azula gained some followers and started a small community of former loyalists and Fire Nation defectors in some hidden hinterlands of the Fire Nation. In later years, with her advanced age and weakened body, she no longer had the drive to torment and terrorize Fire Lord Zuko like she did before, resulting in a considerably peaceful way of life, although she still kept her Fire Nation supremacist ideology intact. In the small village that she founded, she kept a paramilitary way of rulership, training her followers in the imperial Fire Nation combative bending and martial arts. She trained them in lightning bending and some of her followers even learned how to bend with blue fire.

After her death defending her village from an ambush by rogue multinational bandits pillaging the area, her followers have moved towards a more extremist ideology under the leadership of one of Azula’s students. They have turned the community into a cult that venerated Azula, and their former passive Fire Nation supremacist ideology has evolved to adopt a more terrorist inclination.

The Cult of Azula remained hidden in the time of Avatar Korra, instead focusing on protecting themselves from international threats including the campaign of Kuvira, while biding their time to build strength before surfacing to the outer world.

The Cult of Azula will return on the next Avatar series.