The role that Virginia Gov.-elect Charles S. Robb plays next year in the state's U.S. Senate race could have major political implications for him, several of Robb's political advisers said yesterday.

The advisers, who requested to remain anonymous, said that if Robb asserts himself as the leader of the party and backs a winning candidate for the seat being vacated by Sen. Harry F. Byrd Jr. (I-Va.), Democratic leaders might view Robb as a likely candidate for national office.

"Depending on what he sees as his future, it is important that he find a candidate he agrees with and push him to the nomination and election," one Democratic campaign strategist said.

"If he Robb wants to be considered as a vice presidential nominee in 1984," added one potential Democratic candidate for the Byrd seat, "he must show that he can unite and deliver a Democrat to the Senate. If he does that, he'd be in a perfect spot. He'd provide balance to almost any presidential nominee."

Some of those same supporters say Robb's natural inclination will be to stay out of the dogfight that is shaping up as the result of Byrd's Monday announcement that he will not seek a fourth term.

The senator's surprise decision sparked furious maneuvering in both the Democratic and Republican parties. Both parties are expected to select their nominees at state conventions rather than primaries.

Rep. Paul S. Trible, a Tidewater Republican who has been working for the nomination for about a year, met yesterday with GOP activists from three of the state's 10 congressional districts.

Trible, 34, said he will "continue to meet with friends across the state, to determine what is best for Virginia and for Paul Trible." Most Republican leaders concede that because of his early start Trible is the party's front-runner, but some older conservatives within the party, including many who supported Byrd, are working to find an older and more experienced nominee. Their first choice is Gov. John N. Dalton, who leaves office next month.

The biggest obstacle to a Dalton candidacy, said a leading Republican strategist, is Dalton's wife, Eddy. "She has been looking forward for a long time to big money and a chance to travel. Now that he is going to make $200,000 a year by working a six-hour day at a large Richmond law firm , it won't be easy to get him to give that up to campaign all across the state for the chance to move to Washington and make $60,000 as a junior senator."

Trible responded to reports of an impending Dalton draft at the Republican nominating convention next summer by saying, "John Dalton said he won't be a candidate in 1982, and I believe he means what he says."

If Dalton can't be convinced to run, before these Republican regulars will give the nomination to Trible they are likely to look elsewhere: to retiring Rep. M. Caldwell Butler and Fairfax attorney Wyatt B. Durrette. The GOP's nominee for state attorney general, Durrette last month came closer to winning than either of his running mates in the Democratic sweep.

Also mentioned are Trible's Virginia Beach colleague in the House, Rep. G. William Whitehurst, and Army Secretary John O. (Jack) Marsh Jr. of Winchester.

On the Democratic side, the front-runners are considered Andrew P. Miller of Alexandria, former state attorney general, who narrowly lost the Senate race three years ago to John W. Warner, State Senate Majority Leader Hunter B. Andrews of Hampton and former U.S. senator William B. Spong, now dean of the law school at the College of William and Mary.

Robb has close ties to all three of those men: Miller worked in his campaign; Andrews is a key supporter in the legislature; and Spong is the man Robb credits with first sparking his interest in Virginia politics. Although Spong is the least likely of the three to want the nomination, Democratic insiders said, Spong would most likely have Robb's support if he sought it.

Other Democrats mentioned, either by themselves or their friends, include former Del. Ira Lechner of Arlington; Del. Alan A. Diamonstein of Newport News; Del. Alson H. Smith Jr. of Winchester; and State Sen. L. Douglas Wilder of Richmond, the only black in the state Senate.

Miller predicted this week that Byrd's retirement announcement was part of a scenario designed to produce a draft of Byrd at the state Republican convention. Miller said he was told of the scheme by "calls from the Senate last week" and suggested that Sen. Wendell H. Ford (D-Ky.), chairman of the Democratic Senate Campaign Committee, knew of the plan. Ford said yesterday that "there is no substance to it at all." Ford said he, too, had heard the story -- from Miller.

Nonetheless, Miller said that he remains "very skeptical" that Byrd will actually retire. For that reason, Miller will wait until the end of the year before making a decision about whether to seek the nomination.