The phrase “a leopard never changes its spots” means that it’s impossible for one to change their character, even if they will try very hard. The expression, sometimes also used as “a leopard can’t change its spots”, is used to explain the idea that no one can change their innate nature.
Examples in use:
“Brendan: ‘Do you think he’ll ever stop lying to us?’ William: ‘I doubt it; after all, a leopard never changes its spots.’ ”
“The teacher tried to be kind to her students, but a leopard can’t change its spots, she was still very mean.”