While the U.S. is holding tight to every Twitter post the president types about the trade battle with China and every signal of when the partial U.S. government shutdown might end, there's some big news rippling through Asia that's going unnoticed here.

It's the long-forgotten TPP, or Trans-Pacific Partnership, that's been rolling out in since Dec. 30.

While it might take a little time to move the markets -- which were largely edging down in Asia Monday morning -- it will have big consequences, one expert based in Singapore told TheStreet on Sunday night ET.

For the record, by Monday morning in Hong Kong time, most Asian markets were seeing slight declines: Hong Kong's Hang Seng and Singapore's Straits Times Index were edging down by about 1% or more, while the Shanghai Composite Index was sagging just by about .5%. (Japan's Nikkei 225 was on holiday.) Dow Jones Industrial Average, S&P 500 and Nasdaq were also down by less than 1%. Crude oil was down about 1%, and silver by .23%. Gold was up by .15%.

But as the week opened in Asia, the TPP -- officially dubbed the Comprehensive and Progressive Agreement for Trans-Pacific Partnership -- is picking up a new member, Vietnam, long known for its cheap manufacturing. 

This news might be largely ignored in the States, but it could lead to changes globally as the partnership will eventually include 11 nations, including Japan, Singapore, New Zealand and Canada.

"TPP is barely being discussed," said Parag Khanna, author of the upcoming book The Future is Asian, and founder of FutureMap, a strategic advisory firm, over email. The media, said Khanna from Singapore, "should be pushing much harder to ask what the alternatives to not joining TPP and a failing trade war are."

TPP, though pushed by former U.S. President Barack Obama, became politically toxic by the 2016 election, with President Donald Trump calling the deal "another disaster done and pushed by special interests who want to rape our country, just a continuing rape of our country."

But Khanna said the U.S. will lose out.

"The U.S., by not joining TPP, will prove to be a seminal error as the White House miscalculated in believing it would not move forward without the US, but it very much has," said Khanna, who holds a doctorate from the London School of Economics.

While the partnership kicked off two weeks ago with New Zealand, Australia, Canada, Japan, Mexico and Singapore, it will grow in the months to come as Brunei Darussalam, Chile, Malaysia and Peru will join in, following Vietnam's entrance this week.

In the short term, he said, Canada, Japan and other US trade partners are "focusing on taking American market share in the region in agriculture, industrial exports, consumer goods, and so forth."

But in the longer term, he said, trade partners will see the U.S. as "unreliable."

They will also likely "double down" on the Regional Comprehensive Economic Partnership and other trade, he said, "which will further erode America's commercial position in the region. American firms, meanwhile, already see this happening and thus must offshore more to Asia and pursue joint ventures to receive better treatment."

Meanwhile, he said, Brexit, which has a  key vote this week, may have a minimal, but positive effect on Asia.

"Brexit of course will have the worst impact on the UK," said Khanna, nothing that the UK does want to push for trade agreements with Japan, India and other major Asian countries.

"The ripple effects for Asia are minimal, and perhaps even beneficial in that Asian companies will also relocate operations to within the EU, which is its largest trading partner."

Japan's prime minister, Shinzo Abe, is reportedly watching Brexit closely, as major Japanese companies such as Nissan Motor Co., SoftBank Group Corp. and retailer Uniqlo, have increasing presence in the region. 

As for the partial U.S. government shutdown, which has become the longest in history, that could affect Asian business as well.

When asked how the prolonged shutdown could influence air travel, Khanna pointed out that, "certainly from a travel standpoint, Asians have been traveling more intra-regionally than ever before, and uncertainty in the US puts at risk the strong numbers of Japanese, Chinese, Filipino and other Asians who have been reliable travelers to the U.S."

Airlines were mixed on Monday morning in Asia, which Cathay Pacific Airways Ltd. and 

Singapore Airlines Ltd. down slightly and Korean Air Lines Co Ltd up by more than 2.2 percent.