Learn Russian: Она пожертвовала карьерой ради рекорда. - She sacrificed her career for the sake of a record.

In Russian, the verb пожертвовать (to sacrifice) requires the instrumental case for the thing being given up. You can think of it as "parting with" your career. Therefore, the feminine noun карьера changes to карьерой.

Both ради and для mean "for". Why use ради in this sentence?

Ради translates closer to "for the sake of" and is used when emphasizing a significant purpose, a high-stakes goal, or a sacrifice. Для is just a neutral "for" (like a gift intended for someone). Since she is giving up her career, ради perfectly captures the high price she paid for the record.

What case is required after the preposition ради?

Ради always governs the genitive case. That is why the masculine noun рекорд adds an -а to become рекорда.

Could I use the imperfective verb жертвовала instead of пожертвовала here?

You could, but it changes the meaning. The perfective пожертвовала shows a single, completed choice with a final result: she made the sacrifice once and for all. The imperfective жертвовала would suggest an ongoing, repeated process, which doesn't fit as well with giving up an entire career for a specific record.