No Tigers in the Pride Lands
The short answer is no. There are no tigers in The Lion King. The story unfolds in the African savanna, a world of lions, meerkats, warthogs, and other iconic African wildlife.
Tigers, by contrast, are native to Asia. Their natural habitats range from the snowy forests of Siberia to the tropical jungles of India and Southeast Asia. Because The Lion King is firmly rooted in African ecosystems, tigers simply don't belong in the narrative.
So while the film celebrates the circle of life on the African plains, you won't find any stripes from the Asian jungle among its characters.