In Trump's order, he criticized global law firms, saying they play an "outsized role in undermining the judicial process and in the destruction of bedrock American principles."
He also slammed the pro bono work such firms provide, saying they give some Americans access to top legal talent they usually could not afford.
During Trump's first administration, Paul Weiss provided legal assistance to migrant families who had been separated at the Mexico-U.S. border.
A Paul Weiss spokeswoman said the order was mainly focused on Pomerantz, who had not been affiliated with the company for some time.
Another one of Trump's orders, targeting law firm Perkins Cole, is already being challenged.
Perkins Cole had worked with George Soros and Hillary Clinton during her failed 2016 bid. It also had a role in working with a firm that compiled the "Russiagate" dossier against Trump that has since been discredited.