Trump didn't care about the the Asia trade agreement. If those other countries want to get screwed by China, let them. They're big boys and can make their own decisions. He cared more about China screwing America. Would you do a deal with a thief? Why would he do a trade deal with China and those other Asian countries that doesn't include stopping them from stealing our intellectual property? So there was no way he could be involved with it.
China was never a signatory to the Trans-Pacific Partnership, nor was it expected to be: in order to become one, the Chinese government would have had to conform to international trading standards, including protection of intellectual property. The T.P.P. was designed to make it economically attractive for Pacific rim countries to trade with each other profitably within a rules-based system
precisely in order to make them less vulnerable to Chinese influence.
The Bush, Obama, and Trump Administrations all made similar efforts to deter theft of intellectual property by Chinese companies and the Chinese government, as have a number of European governments. Multilateral trade agreements are the most effective way to accomplish this. Improved information security—e.g., better defenses against computer "hacking"—also help, but each new defensive mechanism is likely to be countered with a new offensive mechanism, so the benefits tend to be transitory.