This is Not a Love Story
At no point in Hawkman #1 is Hawkgirl, or his relationship with Kendra Saunders referenced. And that's a good thing. Though the two often go hand in hand, if DC wants to rebuild Hawkman's image, they need to be separated for a bit. Everything about Carter Hall and Kendra Saunders' relationship was problematic. A woman with the soul of Hawkman's lover but without any of the memories was a tough pill for him to swallow, and a majority of their interactions involved him harassing her because, according to him, they were meant to be together.
It was a storyline that very much revolved around his needs and desires. Sure, Hawkman eventually learned to respect Kendra's boundaries, but it also involved him wearing her down. This was still not enough for him, though, so Kendra was killed in Blackest Night and Shayera returned. When Hawkman needed to be taught a lesson in Brightest Day about living for himself and not his girlfriend, Shayera was killed off again. Hawkgirl had no agency in these stories because it was all about Hawkman. It's a story that should not have been OK then, and it would certainly not be acceptable now.
The problematic nature of Hawkman and Hawkgirl's relationship is brought to its logical conclusion in the Injustice: Gods Among Us - Year Five comic book series. In this universe, it is explicitly stated that Hawkman is abusive and manipulative to his wife. She ultimately rejects him and defeats him in combat before Superman later kills him. Despite the fact that he aligned himself with Batman's Insurgency, Hawkman was depicted very much like the bad guy. This version of Hawkman is not too far off from how the character has been depicted for the last 15 to 20 years.
But in this new title, with a new Carter Hall, we have a Hawkman who is independent from his supposed wife and devoid of his past obsessive habits. With Kendra now a member of the Justice League, it won't be long before the two interact in some way, but hopefully Venditti and Hitch can allow them to exist on their own. If Hawkman is busy living his own life, this series will actually have the opportunity to explore who Carter Hall is as a superhero, an adventurer, and as a man. Hawkman and Hawkgirl will be together one day, but we will all be better off if DC takes their time with them.
The Hidden Secrets of Hawkman
Carter Hall may be a new man, but Hawkman is still the same old riddle wrapped in a mystery, wrapped in an enigma. Something is different about Carter's past lives. The old question of "Who is Hawkman?" can't be so easily answered anymore. We know from Metal that his life may not have started out as Prince Khufu of Ancient Egypt as we have always believed, but there is more revealed in Hawkman #1.
Seeking the help of one of DC's bigger mystics, Madame Xanadu, Carter has a vision that details past lives he doesn't even remember having. If you have ever wondered why a man who has been reincarnating on Earth for thousands of years would somehow also be reincarnated on the alien world of Thanagar, this book has the answers -- or, at least, it presents some new questions to be explored. It turns out, at some point over the span of his timeline, he was also a resident of the planets Krypton and Rann. This leads him to conclude that he has actually been reincarnating across time and space, as if he were traveling to some unknown destination.
The vision ends with an image of a post-apocalyptic Earth with large, menacing hawk-like beings standing over the ruins. The story being told in Hawkman is a journey to discover Hawkman's true origins, and the secret could bring about the end of the world. It is up to Carter Hall to figure out what this new threat is and stop it before it is too late. Thankfully, Venditti and Hitch has envisioned a Hawkman who is up to the task.