Update:

Ideas:

(western) She was part of a gang but now that gang has broken up and gone their separate ways after a last big score. The law and the bounty hunters are on their tail. Most never realized she was a woman but one bounty hunter did and he has made it his goal to catch her. Ultimately, he thinks he can use her to get to the rest. A big score for him, enough to retire. 

(viking/fantasy) He is a viking raider leading a small group to raid an elven settlement. She is a priestess. What they don't realize is there is more at work than just this night when his group raids her temple and she is taken as a slave. No, the gods have a use for this viking and she is the key to him saving the world from the evil that is coming.

(historical/fantasy) Scottish clans at war. He is the head of one clan, fighting over land, over the murder of his uncle. She is a selkie, a woman who can change to and from a seal. She is caught by one side and escapes. His clan finds her and assumes she is a spy. All she wants is her coat back so she can return to the sea but her original captors have it. 

(pirate) Their ship is taken over by a pirate. The crew is told to join the pirates or walk the plank and take their chances with the sea. Unfortunately, one of the crew is a woman. The pirate captain is superstitious, women are bad luck on a ship. The dilemma is she is the sailing master/navigator and a damn good one. 

(modern/supernatural) She is a hunter. He is a (vampire/werewolf/mage/etc) Her job is to protect him. There is a war in the city and he is the key to a peaceful end. He has to trust her not to kill him and she has to follow her orders.

(modern/supernatural) She is just a med student. Or that is what she believes. He is her guardian though she has no idea he is there. Thinking a twist on Red Riding Hood perhaps? The wolf protecting her from the hunter and not the other way around. Perhaps she has some magical ability and his kind were tasked with protecting her bloodline. 

(post apocalyptic) The disease ravaged through the world. Small pockets of people worked together, communities set up to help each other. Gardens, scavenging...There are rumours of a facility with a cure but you have to get there, have to find it. He decides to try to find it (perhaps he contracts the disease) and on the way finds her. Will they work together to find the fabled facility?

(near future/futuristic) He is wandering the square, disoriented and confused. Her wiring is going nuts trying to read his system. Someone fucked around in his head, wiped parts...tampered with it. She takes him home offering to help. She is a hacker. He is an assassin/a specialized soldier/etc. Think cyberpunk tech with a some conspiracies and private groups all mixed together.

(thriller/horror/supernatural) The island is steeped in mystery. Disappearances, strange beasts. He has come to research for a book. The islanders do what they can to get nosey people to go away, finding nothing to interest them. This time is different. He has arrived when she arrives. She is there for her father's funeral. She is about to learn a great deal about how her family is connected to the mysteries of the island.