Nothing is in development, but there is a hope!
Fallout: New Vegas

Obsidian CEO Feargus Urquhart says that he would love to work on a new Fallout game if given the opportunity. When speaking with DualShockers, Urquhart responded to a question as to whether he would make a new Fallout game by saying "there's not a question." That is to say, if given the opportunity, he and Obsidian would unquestionably work on a new Fallout game.

For those who may not recall, Obsidian developed Fallout: New Vegas, a game that is one of the favorites of modern Fallout game fans. The problem is that there is a bit of bad blood between Obsidian and Bethesda. When New Vegas was being developed, Bethesda stipulated that bonuses would only be given to Obsidian if the Metacritic rating was 85% or higher. It missed that by just 1%, meaning Obsidian did not receive any bonus. This led to Obsidian being put under financial duress, which then also led to several layoffs within the company. At the time, Obsidian also had to cancel a game that was codenamed "North Carolina."

After the news made the rounds about bonuses being tied to review scores, there was a pretty big fallout throughout the gaming industry. Since then, at least so far as we all know, publishers no longer tie promised bonuses or payments to review scores.

Almost as interesting is the fact that both Bethesda and Obsidian are now under the same umbrella at Microsoft.

"If we ever got the opportunity to make another Fallout game, we'd make it. There's not even a question of whether or not we would do it, it's just: Will the opportunity arise? I hung around at Interplay for probably an extra year because I wanted to work on Fallout more. I love Fallout."
While it is a possibility of an Obsidian Fallout game happening, there aren't any current plans for one. During Fallout's 25th anniversary, Obsidian took to Twitter to praise the franchise, but also deliver some unfortunate news to fans.

Currently, the only plans for new Fallout come from Bethesda directly. However, before that happens the studio plans to finish and release Starfield. They also announced Elder Scrolls 6, a game which is still only in pre-production. In June, Todd Howard sad that only after Elder Scrolls 6 will Bethesda begin working on Fallout 5. At this rate, we will be lucky to see a new Fallout game in a decade's time.