For Earl Dumarest, it always starts with a dame.
Or if it doesn't start with a dame, there's a dame involved somewhere.
In this case case, the dame is named Derai, and she is on Kyle, after running away from her family, because she's afraid of everything. Dumarest is given the gig of escorting her back to her homeworld of Hive, where she is a member of the House of Caldor, one of the ruling families of Hive. On the trip to Hive, Dumarest watches Derai clean out a professional gambler. He intuits that she is a bona fide telepath, and he decides that her survival is best asisted by paying off the gambler. She naturally falls in love with Dumarest; Dumarest, though, is a man with a mission, finding Earth.
Dumarest has his own reasons for travelling to Hive; he's been told that someone on Hive knows something about the mythical world of Earth, a world where Dumarest was born.
But there are intrigues in Derai's family, and the sneaky, dastardly Cyclan are involved with their own agenda. The schemes pull Dumarest back in and induce him to travel with the chiefs of the House of Caldor, and with Derai, to the planet Folgone, where men risk their lives in a deadly competition to run a gauntlet to qualify as one of the few winners, otherwise, they are locked into the playing zone where they starve to death. If they win, they - or the wealthy person who pays for their participation - get planted into a pod where they are slowly absorbed while enjoying glorious hallucinations. In this universe, that's what qualifies as "La Dolce Vita."
As with most of Dumarest's world, you have to marvel at (a) its wanton cruelty and (b) its mysterious economics. After all, wouldn't the City Fathers of planet Folgone, or whoever runs the place, figure out that more people might pay to join in the tournament if they weren't promised certain death if they lost? Whatever the answer, Dumarest's world is a cruel, cruel reality.
Needless to say, Dumarest enters the tournament, and, then, he decides that he loves Derai. Will he marry the girl and accept a place as heir apparent to one of the wealthy clans of Hive? Will he give up his lonely quest through a cruel and uncaring universe to find his lost homeworld?
The only hint you'll get from me is that this is Dumarest of Terra #2 and there are another 31 books to go in the series.
Read the book. It's filled with cliches, but it is fun as a "throwback" to a time when men were men and lived by their own rules in a callous, indifferent universe, and only occasionally fell for the dames.