People Express Inc. will acquire Frontier Holdings Inc., the Denver-based parent of financially troubled Frontier Airlines, for about $300 million -- or $24 a share -- in an agreement announced yesterday by both companies.

The no-frills, low-fare airlines based in Newark, N.J., outbid Texas Air Corp., the Houston-based airline that a few hours earlier had increased its bid to acquire Frontier Holdings to $275 million or $22 a share.

In a move that would give People Express about 50 percent of Frontier's outstanding shares, the two companies also announced that People Express had agreed to purchase 5.2 million shares of Frontier stock currently held by RKO Enterprise Inc., Frontier's largest shareholder, and was granted an option for up to 2.1 million authorized but unissued shares of common stock of Frontier. Both transactions would be priced at $24 a share.

If the deal is completed, People's acquisition of Frontier would mark the second unsuccessful takeover attempt this year for Texas Air President Frank Lorenzo, who was outmaneuvered by Carl Icahn in a bid to acquire Trans World Airlines Inc. this summer.

"Until we've seen the papers, we have no comment," said Clark Onstad, vice president of Texas Air Corp. People Express executives could not be reached yesterday for further comment.

Texas Air said yesterday that it increased its bid for stock in Frontier Holdings Inc. from $20 to $22 a share. On Sept. 19, Texas Air, parent company of Continental Airlines and New York Air, launched its offer to buy Frontier's 12.5 million shares of outstanding stock for $250 million.

The Texas Air offer was an attempt to outbid a coalition of Frontier labor unions that had offered $17 a share for control of the Denver-based carrier.

The union coalition -- the Airline Employees' Association, the Air Line Pilots Association, the Association of Flight Attendants and the Transport Workers Union -- supported the People Express offer and agreed to end their leveraged buyout attempt, according to executives from Frontier and People Express.

The Frontier union coalition last month filed a federal lawsuit to block Texas Air's attempted buyout. The suit alleges Texas Air's Lorenzo was making a "blatant attempt" to trim competition in Denver. Continental Airlines is Frontier's chief competitor in Denver. The case is still pending.

Frontier, the nation's 15th-largest airline, founded in 1946, has experienced severe economic difficulties in recent years and has drastically reduced its operations. In 1983, the company reported a net loss of $13.7 million, while last year that loss increased to $31.1 million.

Earlier this year, Frontier sold about half it jets to United Airlines and then leased them back.

In outbidding Lorenzo, People Express Chairman Donald C. Burr, was pitted against his former boss. People Express was created in 1981 by five former officials of Texas International Airlines, the predecessor of Texas Air.

People Express, the discount airline pioneer, is noted for its low-cost, high-volume coverage of the Eastern Seaboard. The airline also has launched intercontinental and cross-Atlantic routes, entered the competitive Chicago market and just announced nonstop service between California and Belgium.

Since 1981, People Express has grown to serve 49 cities from its Newark International Airport hub.

Analysts said the acquisition of Frontier allows People Express to quickly move into western markets.

People is noted for its high-volume coverage of heavily traded routes along the East Coast. The airline also operates daily flights to London and Brussels from Newark. The airline said yesterday that it will begin $249 nonstop service between San Francisco and Brussels, Belgium, next month.

Executives from both companies said in a statement that Frontier would be operated as a separate company and would maintain its current structure and identity.

The acquisition and purchases are subject to various regulatory approvals, including approval by the U.S. Department of Transportation and formal ratification by Frontier's labor unions.