The Hawkmates really are confusing! They’ve been retconned to seven hells and back. Not even most writers get them! Hawkman (2018) is the best place to start. It gives you a concise, easy to understand explanation of the Hawks’ reincarnation cycle. If you want the full story, however, then read on!
The Hawkmates are reincarnating soulmates from across time and space. First, there was Carter Hall (Hawkman) and Shiera Saunders (Hawkgirl), a pair of archeologists from Earth. They can be found in golden age comics like Flash Comics (1940) and All-Star Comics (1941). Because they're so old, there can be some really poorly aged and racist content. Read at your own digression. If you want something more modern, then there's Thrilling Comics (1999), Justice Society of America (1991) and Justice Society of America (1992).
The silver age gives us Katar Hol (also Hawkman) and Shayera Thal (Hawkwoman) from the planet Thanagar. Crisis on Infinite Earths happens and now Katar and Carter exist on the same planet at the same time. A little confusing, but that's barely scratching the surface. You can find them in Hawkman (1964) and Hawkman and the Atom.
Hawkworld, featuring Katar and Shayera, is one of my favorite comics ever and you should read it! The book was originally supposed to be an Elseworld set in a different universe, but it was so popular that it became canon. The thing is though, it was set in the modern day and there was already a Katar Hol flying around. Turns out, that was actually Fel Ander, a Thanagarian spy disguised as Katar! He's the Hawkman in Justice League International. He groomed a woman from Earth named Sharon Parker to be his wife and Hawkwoman. Hawkman fans still see pre-crisis Katar and Shayera as still Katar and Shayera.
Zero Hour happened and things got weird. In an attempt to make things less confusing, Carter, Katar, and Fel fused into one Hawkgod. No one liked it and it made things more confusing, so confusing that DC banned the Hawks from ever appearing for 5 years.
They would return in JSA (1999). Kendra Saunders is Shiera's great niece and inherited her wings. After her parents died, she committed suicide, but was brought back. This is because Shiera's soul entered her body. Carter also comes back later, and the two have adventures in Hawkman (2002).
Flashpoint happens. Katar Hol from Thanagar is there and uses the name Cater Hall as an alias. Kendra is also there.
Doomsday clock undoes that and we get Hawkman (2018). In it, it is revealed that the Hawkmate reincarnate across and space! Meaning, Carter is a reincarnation of Katar! Shayera also comes back. She and Kendra can exist at the same time because they were born on different planets.
Carter and Kendra are currently in JSA (2024). If you have any more questions, feel free to ask @hawkgirlz or my main blog, @fall-of-fall . Happy reading!