Time Inc., the publishing conglomerate that owns the Washington Star, has acquired a 20 percent interest in Kansas City-based Universal Press Syndicate in exchange for the assets of the Star Syndicate, plus an undisclosed amount of cash.

The Star gets the right to run "Doonesbury," the popular political cartoon as well as other comics and features now carried by The Washington Post, according to James Andrews, chairman of UPS.

Andrews refused to reveal precise financial details, as did Time Inc. However, industry sources estimated the acquisition probably cost Time Inc. about $1.5 million. Time originally had tried to buy the entire syndicate, Andrews said yesterday, but he and President John McMeel refused because "we like our independence."

Andrews, 42, and McMeel, 43, founded UPSin 1970. Their first real success was Garry Trudeau's controversia Pulitzer Prize-winning strip, "Doonesbury." @ups also syndicates the comics "Kelly & Duke," and "Ziggy," as well as Pulitzer Prize-winner Paul Szep's political cartoons, the "Gold Earth Almanac" and weekly "Mini-Page" features, now carried by The Star.

The Star now syndicates columnists Mary McGrory, James J, Kilpatrick and William Buckley. Andrews said all of these would be syndicated under the UPS credit line, probably with an aftermention that they originated in the Washington Star. Some Other Star writers will be dropped from syndication, although he declines to name them because they have not yet been notified. The Star Syndicate's president and editor, Harry E. Elimlark, 69, will remain as editor, but Andrews and McMeel will run the show.

Competitors place Universal Press about fifth in the field behind the King, United Features, Field Enterprises and Chicago Tribune syndicates. Andrews said the merger withthe Star Syndicate would put UPS well ahead of the Chicago Tribune Syndicate.

UPS plans to establish offices here and New York. Andrews said his company intends to begin syndicating features on a spot basis from other Time Inc. publications including Sports Iilustrated, People, Money, Fortune and Time magazines.