The Arlington County Board yesterday approved a 14-year early extension of its cable television franchise agreement with Arlington Telecommunications Corp. (ARTEC), ending at least momentarily one of the county's most fractious and time consuming debates.

The new agreement, which amends the board's decision in July to extend the ARTEC franchise six years from its scheduled expiration in 1985, is expected to cost the company an estimated $11 million in franchise taxes, new equipment and financial support for public cable facilities and programing. It also means a probable increase of $1 or more within the next few months to the monthly $9.95 fee Arlingtonians pay for basic cable.

ARTEC, which entered its original agreement with the county in 1975 and became fully operational a year ago, asked the board earlier this year for the extension, saying it needed a guarantee of continued operations before it could get long-term financing on about $6 million in short-term debts.

The company now serves about 20,000 Arlington households, or about 36 percent of the county's potential subscribers. ARTEC ran into trouble in its infancy after the death of an important company officer and has been under attack from various segments of the community for failing to meet its contractual agreements with the county.

It remained unclear yesterday how the agreement might be affected by legislation now before Congress that would effectively strip local governments of power to regulate cable service charges and limit fees against monopoly franchise.

"I don't know," said John Evans, ARTEC's executive director. "What we have is a contractual arrangement. We'd have to have our lawyers look at that." Arlington levies a 4 percent tax against ARTEC's gross receipts, about $2.5 million last year. The new agreement also calls for county board review of all proposed rate increases.

ARTEC officials maintained that the company's failure to complete its contractual obligations was caused primarily by unforeseen high interest rates and fluctuations in financial markets. Board Chairman Stephen H. Detwiler, a banker, was sympathetic and led efforts to get quick approval for the extension. However, Detwiler's two Republican colleagues on the board, Walter Frankland and Dorothy Grotos, continued to fault the company yesterday.

"If a company is doing so poorly, I wonder what service we are doing to the community by not opening the process up to other competing companies," said Grotos, who cast the lone dissenting vote in the decision to grant the extension. "It seems we have taken the position that what's good for ARTEC is good for Arlington and I'm not sure that's the right rationale."

The board spent six hours yesterday eliminating or reducing several new financial obligations proposed by the county staff to provide for originating local cable programing and providing cable equipment to schools and public institutions.

The new agreement gives the company nine months to secure financing and fulfill obligations for providing equipment and financial support for local productions.