I bought Innovation.
While a Haggler is in play, I bought Province. I gained and set aside another Haggler. I played it.
Do I gain another card cheaper than Province?
Yes.
When you're in the window for resolving effects that trigger on a particular thing, new things that show up also work. This goes back to Secret Chamber / Moat - I play Militia, you use Secret Chamber, you get Moat from it, you use the Moat on the Militia.
The part I don't follow is hagglers text says "while this is in play when you gain a card" how can the it be in play before the province is gained?
I can kind of follow the secret chamber most reasoning, but I still struggle with it.