When you use, "My older sister has been married for three years," you imply that your older sister married three years ago & is still continuing her marriage. When you use, "My older sister got married three years ago," you refer to the single event in time (her marriage) which happened three years ago - however, that doesn't mean that she's still in the marriage.

"My older sister has been married for three years" is the grammatically correct sentence. However, there are mistakes in the second sentence. Instead, you can say "My older sister got married three years ago".

The first one is correct. The second one is not correct. You could say 'My older sister got married three years ago'.