UNC Resources Inc., in an effort to move quickly from a troubled past to a profitable future in high technology, yesterday announced it has reached an agreement to buy TRT Communications Inc., a subsidiary of United Brands Co., for $56 million.

The acquisition of the small but rapidly growing international data-transmission company will be made through a leveraged buyout in which UNC will put up $11 million through a subordinated loan and equity.

A major bank will provide the remaining $45 million in debt, which will be secured by TRT's assets.

The purchase, subject to the approval of the Federal Communications Commission, is expected to be completed this fall.

It is the first of several acquisitions now being considered by the former uranium mining and processing company, which has just climbed out of the red after years of financial woes.

"This is just the beginning of some acquisitions," said UNC President Dan A. Colussy yesterday in an interview minutes after he had signed the agreement on the acquisition.

"We're out to change the character of the company, and this is how we are going to do it. Any company that is in the mainstream that has had a good past and a good future" is a candidate for a merger, he said.

"We're looking at a lot of acquisitions" of companies in the technology and services field, said Colussy, who became UNC's president Jan. 1. When assuming the position, he was given the directive to bring UNC back to financial health.

TRT has been up for sale for some time, a United Brands spokeswoman acknowledged yesterday.

"It's not the business we're in," she said. "We're focusing on the banana and meat business." Last year, the company considered selling off the company in a public stock offering, but that idea fell through after the demand for newly issued stock, especially in high-tech companies, dropped.

"It's not been a secret that TRT has been for sale for several months," she said.

Under the acquisition agreement, TRT's managers will stay on at their Washington headquarters. Although UNC, a Falls Church company, will acquire all of TRT, about 15 percent of the initial equity will be held by present management to ensure that they stay, Colussy said.

"I will not be participating in the day-to-day management of TRT," Colussy said. In a leveraged buyout, borrowed funds are used to acquire the company and the borrowing is repaid later with proceeds from the acquired company.

TRT is an 82-year-old communications company that was begun by United Fruit Co. -- now a part of United Brands -- to provide a communications network for its Latin American banana operations, mainly to find out when the crop was ready for shipment.

After unsuccessfully trying to sell the company -- then called Tropical Radio and Telegraph Co. -- in the mid-'70s, United Brands decided to open the network to other users, making it a competitor to other international telecommunications companies transmitting telexes and high-speed data, such as RCA, Western Union and ITT.

Today, TRT has grown into a company with $122.2 million in annual sales, on which it earned $6.37 million in the fiscal year ended March 31, with about a 13 percent share of the international outbound data and telex market. It has just begun to expand into the international voice market, providing service to the United Kingdom.

TRT also has a 43 percent interest in International Satellite Inc., which is awaiting FCC approval to develop and operate a private international satellite system between the United States and Europe that would provide competition with Intelsat.

Colussy said he planned to keep TRT in its specialized telecommunications niche. "We will concentrate on the niches. We have no intention of taking on any giant head-to-head."