What is the grammatical structure after the comma?

This could be an instance of ellipsis:

Merriam-Webster the omission of one or more words that are obviously understood but that must be supplied to make a construction grammatically complete

The complete version of the clause would have been:

the gap will be $3.7 billion, [which is] a billion dollars more than they had predicted just two months ago.

[which is] was [elided] omitted to make the sentence more compact.

My reflex is that your instinct on it being an adjective phrase is too straighforward to be false. It is an adjective phrase modifying the noun "$3.7 billion."

I do not think there are any absent or implied words. The fact that words can be sensibly inserted does not mean they are necessary, directly or by implication. I think there are probably a lot of adjective phrases that could absorb some additional connective tissue without gaining much weight, but that makes no imperative to increase their diet.

I am not a grammarian and am wrong with shocking frequency.