Hi Shou,
The subject of the verb is "that". This word is a demonstrative pronoun and in turn describes the President's business connections in many countries.
Donald Trump has business connections in many countries that will put U.S. national interests in jeopardy.
We can separate it right between the first idea and the second.
Donald Trump has business connections in many countries. That will put U.S. national interests in jeopardy.
If you still want a comma, you have to use a conjunction.
Donald Trump has business connections in many countries, AND that will put U.S. national interests in jeopardy.
Hope this helps.
Cheers, Lance