There have been many theories of Scar being Nala's mate while some others even think Nala is his own daughter!
What's your own theory?
Well, I'm just gonna follow TLKoB and say that they weren't mates but Scar wanted them to be.
Theory:
Nala ran away because Scar wanted her to be his queen (and mate with her) so she could find help and stop this nonsense. Then I guess, if the Outsiders were at the Pride Lands, Scar made Zira his queen not because he wanted to, but he needed a queen and Zira seemed to be the most royal lioness. Otherwise I'll say that Scar didn't have a queen during his reign, because I doubt Nala would ever make Scar her mate.
And about her being his daughter, I doubt that Mufasa would betroth his cub's cousin, especially if it was Scar's daughter. Plus, Scar would let Nala get eaten by the hyenas on the Elephant Graveyard! So, I really doubt it that he's her father.