Karolsen

SuperGuardian is the het ship between James Olsen and Kara Zor-El on CW series Supergirl.

Canon
TV series

James and Kara meet when she starts her job as Cat Grant's assistant at CatCo Worldwide Media, and Kara is instantly attracted to James, the Art Director. Kara develops a crush on James, which only intensifies as the two become good friends. Before Kara can tell him how she feels, James' ex Lucy Lane rolls into town from Metropolis and they rekindle their romance, as Kara doesn't wish to stand in the way of James being happy. While James is hesitant about dating Lucy again, they do get back together and have a good thing for a while, until Lucy starts feeling that James is not invested in the relationship. After talking with Kara, Lucy realises that James doesn't let her in and she breaks up with him for good, also well aware that James returns Kara's feelings for him.

Fanon
Some media has criticised the unfounded move to never have Kara and James get together, just for her to get together with a new character.
 * I’ve watched as Kara — a girl who needed her friends, who needed her job at Catco to remain grounded — became unrecognizable. It’s not just that Mon-El has done horrible things or that Kara broke up with James for, I can’t even remember the stupid reason

Trivia

 * In the comics, James and Supergirl marry at one point!