UAL Inc., parent of the nation's biggest airline, said yesterday its profits rose modestly in the third quarter from a year earlier, while smaller and long-struggling Republic Airlines reported a $14.6 million profit, reversing last year's devastating losses.

In the publishing group, The Tribune Co. yesterday reported its third-quarter net income increased 123 percent to a record $27.9 million, compared with $12.5 million a year ago. The Times Mirror Co. put its net income for the period at $46.8 million, a slight increase over the $45.3 million earned in the same quarter last year.

UAL Inc., holding company for United Airlines and other ventures, said profits rose 6 percent in the third quarter to $66.7 million from $63.1 million a year earlier. Profits per share, however, fell to $1.75 from $1.77, as the average number of shares outstanding increased.

Revenue rose to $1.83 billion from $1.64 billion a year earlier, UAL said.

For the first nine months, UAL said profits rose 251 percent to $215.3 million ($5.70 a share), from $85.9 million ($2.32) a year earlier. Revenue rose to $5.3 billion from $4.36 billion a year earlier.

In the first nine months of this year, UAL said it was helped by an extraordinary gain of $18.5 million (53 cents). But the nine-month results also include a $50.6 million expense related to termination of employe incentive programs.

UAL also owns Westin Hotels, Mauna Kea Properties and GAB Business Services.

UAL Chairman Richard Ferris said in a statement that fare cuts in approximately two-thirds of the markets serviced by United Airlines through most of 1984 and a $38 million "back pay" award in a lawsuit against the carrier cut into the company's third-quarter earnings.

Spokesman Chuck Novak said the huge earnings increase for the nine months reflected an $18 million gain because of debt retirement and also reflected a strong performance in the first two quarters of the year. In 1983, the company reported a first-quarter loss and a marginally profitable second quarter, largely because of fare cuts in its airline service, he said.

In a separate release from its headquarters in Minneapolis, Republic Airlines reported profits of $14.6 million (36 cents a share), in the third quarter, compared with a loss of $12.2 million in the third quarter of 1983.

It said employe wage concessions won earlier this year and other cost-cutting measures were largely responsible for the profit, which came even as revenue fell to $385.5 million in the third quarter from $392.9 million a year earlier, Republic said.

For the first nine months of 1984, Republic posted a profit of $40 million ($1.04), compared with a loss of $115.1 million a year earlier.

Revenue rose to $1.19 billion in the first nine months from $1.13 billion in the first nine months of 1983, Republic said.

Stephen M. Wolf, president and chief operating officer, said he was encouraged by the results.

Earnings per share for Chicago-based Tribune Co., whose holdings include its flagship Chicago Tribune newspaper, the New York Daily News, WGN-TV and WGN-Radio and the Chicago Cubs baseball team, rose 97 percent to 69 cents from 35 cents in the third quarter of 1983.

The Tribune Co. reported total revenue of $432 million for the quarter ended Sept. 23, an 11 percent increase from $390 million a year ago.

In the first nine months, net income increased 90 percent to a record $67.1 million from $35.2 million a year ago. Earnings per share climbed 68 percent to $1.66 from 99 cents in the period last year.

The Times Mirror Co. net income for the first nine months of 1984 was $149 million, compared with $117.9 million in 1983 earned by its newspaper, book, television and forest product divisions.

Although the net income increased in the third quarter, the operating profits of $88.7 million were 6 percent less than the $94.5 million reported in the comparable period in 1983, the company said.

The drop was attributed to a two-month strike at an Oregon newsprint mill, the cost of covering the Summer Olympics and changes in book publication schedules.

Operating profits over the first three quarters, however, increased to $299.5 million over the $251.4 million recorded in the first nine months of 1983.