Learn Spanish (Spain): Tras la agresión, la víctima fue al hospital. - After the assault, the victim went to the hospital.

Both mean "after", but tras is slightly more formal and often implies an immediate sequence of events, much like saying "following the assault" in English. It is very common in journalism and written narratives.

Does agresión just mean "aggression" as in being angry or hostile?

Not exactly; it is a partial false friend. While it can refer to an attitude of aggression, in legal and news contexts like this sentence, una agresión translates to a physical "assault" or "attack".

If the victim was a man, would we change it to el víctimo?

No, víctima is always feminine. It is what grammarians call an epicene noun: a word with a fixed grammatical gender that can refer to people of any biological sex. You will always say la víctima.