WASHINGTON—A company owned by Joel Zamel, an Israeli entrepreneur whose work has drawn the scrutiny of special counsel Robert Mueller, formed a strategic partnership with a data firm for President Donald Trump’s campaign in a joint bid to win business from the U.S. government and other clients after the 2016 election, according to people familiar with the matter.

The Psy-Group, one of Mr. Zamel’s firms, signed a memorandum of understanding with Cambridge Analytica LLC, a digital media firm that helped propel Mr. Trump to the presidency, these people said. Facebook Inc. in March suspended Cambridge over allegations that it improperly harvested the data of millions of Facebook users, accusations that in part led to the firm’s closure earlier this month.

The Dec. 14, 2016, memorandum, as described to The Wall Street Journal, outlines a partnership whereby the two firms could cooperate on a case-by-case basis to provide intelligence and social-media services, or pitch business to an array of clients.

A person familiar with the work of Psy-Group, a private intelligence firm, said the partnership was intended in part to help win government contracts—something that Cambridge and its parent company, SCL Group, were aggressively seeking to do as their allies in the Trump administration took power, according to people familiar with the efforts.

The existence of the memorandum is an example of how the president’s allies sought to gain entry and influence in Washington after the election.