Ese +2, finaliza al final de turno, el pj debe estar activo, (algunos comentarios, no oficiales)
Unless otherwise stated, effects last until the end of the turn.
Cards that say "while active" are "while active" effects. It triggers when it says it triggers, which is each time you use an action die.
Adding reminder text, this card should fully say:
Each time you use an Action die, Baron Zemo gets +2A until the end of the turn

Edit: The D&D Adventurer cards add an Experience token, which indicates that the effect persists.
-Is Baron considered a while active effect?
Page 11. "All effects end (except "While active" and "effects that occur at the end of turn")."
-No
-So if it is not a while active ability, when do you give it +2? Does the card get it each time you play actions whether the character is in the field or not?
-Card effects don't trigger if the character isn't in the field. It triggers when he is in the field when you use an Action die.
In the DC rule book it says "all effects end (except while active effects)."
Unless is adds a token, it is understood to be until end of turn and needs to be active. (experience does need to have an active character to have the token added.)
-An example of "While active" is Captain America - Man Out of Time
-Yes, i understand this.
Can a triggered effect occur if a character isnt in the field?
But are there any 'while active' effects that dont have that text on them?
-Can a triggered effect occur if a character isnt in the field?

Not unless explicitly stated.
Are there any 'while active' effects that dont have that text on them?

I don't believe so. Any effect that has a trigger only lasts for that turn. They never extend beyond that, unless explicitly stated (like Experience tokens or Thanos - Infinite).

Never assume something lasts forever. It will always say that it persists.