The Trump family has struck a deal with a Saudi-based real estate company to license its name to a housing and golf complex that will be built in Oman, renewing a swirl of questions about former President Donald J. Trump's mixing of politics and business just as he appears poised to announce a third presidential candidacy.

News of the deal, the first such international marketing agreement the Trump Organization has negotiated since Mr. Trump left the White House, emerged as the former president already faces a string of investigations into his business.

The project is slated to be built in Muscat, Oman, on a hillside adjacent to the Gulf of Oman, and will include a golf resort, villas and two hotels, a company executive said.

The Trump family is teaming up with Dar Al Arkan, one of Saudi Arabia's largest real estate companies, for the project.

Deals like this — in which the Trump family gets a cut of condo sales or golf course revenue in exchange for allowing its name to be used — used to be a major source of revenue for the Trump Organization before Mr. Trump was elected president.

But the family agreed to not sign any new international deals while Mr. Trump was in the White House, and it has been slow to negotiate any new ones since he left office as civil and criminal investigations have distracted the Trumps and put a crimp in the company's growth.

The new deal comes as the Trump Organization is inundated with legal problems. It is on trial in State Supreme Court in Manhattan for criminal tax fraud charges, and it is fighting a lawsuit from the New York attorney general, Letitia James, who accused Mr. Trump, his company and three of children of fraud.