If I attack a battlefield that has Overzealous Fan while playing Diana, can I use my Diana legend to pay for Gust before my opponent has the chance to activate Overzealous Fan ability trigger?

Yes, but it depends on one key timing detail: the opponent's decision to use Fan's ability happens before you get a window to respond.

Here's the exact sequence:

1. You move to attack → Showdown begins → you (the attacker) gain Focus per Rule 345.
2. Overzealous Fan gains the Defender designation → its "When I defend" trigger condition is met.
3. The opponent immediately chooses whether to use the ability. Per the Unleashed update (FAQ #9611, Rule 383.3.b.1), if they choose to use it, they kill the Fan upfront as a cost to place the trigger on the chain — before any response window. There is no gap where you can Gust first.

So there are two paths:

• Opponent uses Fan's ability → Fan is killed as the cost upfront and goes to trash. You can still activate Diana's legend ([Reaction], adds resource immediately) and play Gust ([Reaction]) during the Closed State — but Fan is already dead and can't be Gusted (it's not at a battlefield anymore). Gust would need another valid target.

• Opponent declines to use Fan's ability → Fan stays alive, no trigger goes on the chain, and the Showdown returns to Open State. You still have Focus. You can activate Diana's legend to generate energy, then play Gust (both as [Reaction] or during Showdown Open), targeting and returning the Fan to hand before any other trigger occurs.

Bottom line: If the opponent wants to pop the Fan, they do it immediately with no window for you to preempt it. If they choose not to (or hesitate on a "may" ability), you have a clear window with Focus to Gust it away using Diana's energy generation.