Cable television has become the latest focus of a power struggle between Montgomery County Executive Charles W. Gilchrist and the new County Council majority.

This most recent rift threatens to delay implementation of the cable franchise agreement with Tribune-United of Montgomery County. It also comes amid indications that Gilchrist's relationship with the council has reached its lowest point since the election last fall.

The debate centers around whether the council or the executive should control public access to cable channels, the grant money available to groups wishing to use those channels, the location of cable facilities and the rates charged for the various cable services.

The county's existing cable television law gives all those administrative powers to the executive. But yesterday, council member David L. Scull introduced a package of proposals that essentially would give the council ultimate authority over virtually every aspect of cable television in Montgomery.

The council has until May 24 to ratify the contract with Tribune-United, and Scull has made it clear he wants his proposals enacted before then. He is also backing a separate proposal to extend that deadline. Explaining his proposals, Scull said, "These are areas where it seemed important to have the local regulatory commission--namely us the council --have an approval role."

John A. Hansman, the cable TV project manager on Gilchrist's staff, said, "It's basically a question of the council deciding that there should be a much stronger, much more pervasive council role than now exists." He added that Gilchrist believes the council should have some say over cable, but Scull's package "is going further than makes sense. It simply goes too far."

The debate over administering the cable contract could determine whether county residents will have to wait still longer for cable TV, already at least a year away.

Last year Gilchrist ran on a Democratic primary slate opposing Scull and his three council allies, and since the election--after some initial public displays of harmony--the relationship has steadily deteriorated.

Another sign that the executive's relations with the council have chilled came yesterday when Gilchrist dashed off an angry letter to Scull and his allies for eliminating a county attorney's job from the 1984 budget.

Gilchrist called the action "vindictive," since the council majority eliminated the job after receiving a series of adverse opinions from the county attorney's office. Saying he was "appalled and repelled," Gilchrist wrote that "good government in Montgomery County received a serious setback by your deed."