And how to take Azira as a companion?
Azyrran?
First you have to earn her trust - or just dominate her. Things that can contribute to the former: friendly mutualistic sex and defeating her in a spar without having sex with her afterward. Things that can contribute to the latter: defeating her in a spar and then having sex with her. Pick one of those two paths and do the options that result in that path repeatedly.
Next, you have to have done some prerequisites. You need to have spoken to Brother Sanders at least once, and you need to have defeated the Alraune - subjugating her or killing her, either's fine.
If those two things are done, you may find that Azyrran asks you for help with her hive-sisters, who've been corrupted by Kasyrra. You then ask Sanders, who tells you that a paladin is nearby. Travel south of Hawkethorne to find Liaden, said newly-arrived Lumian paladin. Then, meet them at the hornet hive in the northwestern Old Forest and complete the quest.
While in the dungeon, there are two potential outcomes. You can backstab them by kicking them into the corrupted honey before it's purified, making them into bimbos like the rest of the hornets; this prevents Lia from going to Hawkethorne and permanently locks out Azyrran from being a companion. Or you can follow Azzy and Lia's request, help them purify the hive, and receive the opportunity to recruit Azzy as a companion; Lia also comes with extra content, including joining you on the quest for the Dawnsword and joining you in a lesbian threesome (actual lesbian - pc must have she/her pronouns) with Azzy. (She has even more content coming down the pipeline, too.)
Companion Azzy can also be temporarily made into a bimbo instead of her normal Hive Knight personality for extra sweet adorable head-empty-heart-full (including dialogue and combat changes), although you're certainly free to keep her a Hive Knight if you wish. She also is very snuggly, has plenty of honey, and loves to give pets.
The whole questline is a little complicated, but there's
a handy Wiki article that can walk you through it.