The Post asserted that:
"[...]entering into a new TPP could unify Trump with other trading partners and put new pressure on Beijing to either allow more imports into China or risk being alienated by other Asian countries, that would now received new trade benefits as part of the deal."
Actually, the countries in the TPP will receive relatively few "new trade benefits" as a result of the TPP. Six of the other eleven countries in the pact already have trade deals with the United States, which means there are very few remaining barriers to be reduced. (One of the other five countries is Brunei, whose trade patterns will probably not cause China's government to lose much sleep.)
If the pact was intended to hurt China, its designers did not do a very good job. It has lax rules of origins requirements. In some cases, for example most car parts, an item with as little as 35 percent value added from TPP countries could qualify for preferential treatment.
This means, for example, that car parts produced in China, with Vietnam adding 35 percent of the value (possibly in a Chinese owned firm) would get preferential treatment under the TPP. Since these requirements are difficult to enforce rigorously, it is likely that some items with as much as 70 percent value-added coming from China will get preferential treatment under the TPP. That does not sound like an effective way to exclude Chinese products. (NAFTA's rules of origins for car parts required 62.5 percent of the value-added to come from the countries in the pact.)
The TPP also includes provisions that will make member countries pay more money for prescription drugs due to longer and stronger patent and related monopolies. It also includes provisions on e-commerce that would likely make it more difficult to crack down on the sorts of abuses we are now hearing about from Facebook. These features, which are major parts of the pact, are not likely to help the United States build an effective coalition against China on trade or anything else.
The piece also tells readers that Trump has:
"[...]shown a general reluctance to enter into multilateral trade deals because he believes these allow the United States to be ripped off."
It is not clear how the Post knows what Trump "believes." It can tell readers what he says, but given the frequency with which he reverses his positions, it seems unlikely he believes anything.