The 2019 remake The Lion King hints at another way Scar got his injury. In this version, it's never explicitly stated but heavily implied that Scar challenged Mufasa.

One lion will always kind of be off in the shadows. We were trying to use those animal truths to underpin the story so we sort of figured Scar and Mufasa couldn’t really be from the same gene ...

The Lion King prequel will dig into the backstory of Scar, Kelvin Harrison Jr. has teased. Harrison Jr. is voicing the future Disney villain in the film, which is set to tell the story of Mufasa.