Hawkman was unique in the Silver Age among all heroes, as he arrived on Earth already married. From a writer's point of view, single characters are more interesting as they're free to form new romantic relationships, or continue old ones, while married characters have to be faithful to their existing partner.
Enter Mavis Trent. In Brave & Bold #34, Hawkman and Hawkgirl meet up with Commissioner Emmett and reveal their real identities as policemen from Thanagar, come to Earth, initially to capture a shape-shifting crook named Byth, but eventually to study our police methods. In fact, not only did they confide in Commissioner Emmett, but he was instrumental in giving them their secret identities while on this planet:
But when Hawkman (as Carter Hall) meets one of his employees, he picks up a clue:
It's such a rare bird that it doesn't exist on Earth, which is why Carter is interested, although it's pretty obvious that Mavis is interested in something else, and a publicity man suggests that Carter and Mavis go on an expedition together to track down the oddity. But Shayera scotches those plans:
But even after learning that Carter is married, Mavis is not deterred:
The subplot in that issue ends somewhat oddly, with Carter and Mavis exploring Hawk Valley (with Shayera as a chaperone) in an unsuccessful attempt to find the rare bird (which was the criminal that Hawkman and Hawkgirl had originally come to Earth after).
In the second tryout issue (Brave & the Bold #35), Carter is surprised when Mavis hugs him for sending her flowers (because he didn't). Shayera is not amused:
Mavis' photos of rare animals shows a chance of breaking into the big time in the second story in B&B #35:
So she's a catalyst for the stories, at the same time as she appears to be something of an antagonist to Carter and Shiera (as they are renamed by Commissioner Emmett. I should mention that although Joe Kubert makes Mavis look quite attractive, there is no hint that her desire for Carter is returned in the stories, and while Shiera clearly gets a little frosty at times, it's always directed at Mavis and not her husband. And at the end of the story, she's no longer quite so enamored of Carter, as the new man in town:
She continues her role as catalyst in B&B #36:
Later, it turns out that the guy she was suddenly snuggling up to in that sequence was after her ring, which leads to this bizarre bit:
Comments: The idea of a femme fatale in DC is pretty far ahead of the times, although I suspect kids were used to seeing this type of subplot on TV comedies (in which the husband/wife always remained faithful). Lois Lane and Lana Lang's rivalry is different, for the simple reason that Superman isn't married to either of them. In later issues (as we'll discuss in future volumes of the Mavis Trent Chronicles), DC did rectify this problem by having Commissioner Emmett tell Mavis that Hawkman and Hawkgirl were not married. But that is a tale for another day.