"It paves the way for a new chapter for bilateral modern and mature partnership,firmly grounded on deeply held democratic values, common interests and shared aspirationsI" I think it can be read both ways. I think one comma makes the difference. I think there is a silent comma, that belongs after new chapter. If you read the sentence that way, without "for bilateral modern and mature partnership," you can see that the sentence actually still makes perfect sense: "It paves the way for a new chapter, firmly grounded on deeply held democratic values, common interests and shared aspirations.

The partnership (noun) is deeply grounded (adjective). The noun and the adjective which describes it are grouped together. The partnership is grounded because of democratic values.

Its the partnership (I think you might be talking about the new US/Mexico agreement) that is "grounded on". New chapter simply means its a new start/beginning.

I think 'grounded on...' refers to the partnership, because of the elaboration that follows. A partnership is a bond between multiple parties; 'Common interests' and 'shared aspirations' are both traits that apply to a group of multiple parties as well. A chapter is one, individual thing, it can't hold traits that apply to groups.