I read these back in the day, probably when they were new. Moon of Three Rings was first published in 1966 and Exiles of the Stars in 1971. I thoroughly enjoyed them then and they hold up pretty well, better than some others of that period, both from Norton and from others, like Heinlein.
This is one of her Free Trader stories with the main character Krip Vorlund, an assistant cargomaster who gets caught up in planetary politics that also touches the rivalry between Free Traders and the big companies or Combines of the inner planets. The Moonsinger of the omnibus title is Maelen of the Thassa, a wandering race on the planet Yiktor who are little known but not entirely trusted by plainsdwellers of that planet. Krip and his port leave partner are drawn to a beast show, where Maelen puts her little people through their paces with no coercion. Due to political maneuvering, Krip ends up transferred into the body of a barsk, a wild untamed animal of the planet, with the promise of being later reunited with his body. Problems ensue.
In Exiles of the Stars, Krip and Maelen take ship with Krip's ship Lydis and continue their voyaging to deliver cargo. They and the Lydis get caught up in a different planet's politics and religion.
As is often true of Norton's books, the main characters are part of something but still end up outsiders.
One thing I dislike of this edition is the cover art. Most of it is fine, showing Maelen concentrating with her wand of power. But her outfit is much too nearly-naked. I seriously doubt that she would sit cross-legged wearing that minimum bikini bottom. It looks most uncomfortable for that posture. We have grown up a bit since science fiction was marketed to adolescent boys.