Learn Swedish: Hon håller tempot, oavsett vad som händer i loppet. - She keeps the pace, regardless of what happens in the race.

In Swedish, when a question word like vad (what) or vem (who) is the subject of a subordinate clause or an indirect question, you must add the word som right after it. Because "what" is the thing doing the happening in this clause, it is the subject, so we have to write vad som händer rather than just vad händer.

Do I need to add a word for "of" after oavsett?

No, you shouldn't add anything. While English says "regardless of", Swedish oavsett stands entirely on its own. You can place it directly in front of a noun phrase or, as in this sentence, directly in front of an indirect question clause. Adding av after it would be a direct translation mistake.

Could I use trots (despite) instead of oavsett in this sentence?

Not naturally. Trots (despite) is typically used when there is a specific, known obstacle you are pushing through, such as trots regnet (despite the rain). Oavsett (regardless of) is the correct choice here because it points to an unknown or open set of possibilities: whatever might happen during the race.

Why use loppet instead of tävlingen for "the race"?