With Arlington prosecutor Henry E. Hudson almost certain to become U.S. attorney in Alexandria early next year, the jockeying has begun for the job he would have to vacate.

The Arlington County courthouse has been awash with lobbying and speculation on a successor since Sen. Paul S. Trible (R-Va.) announced two weeks ago that commonwealth's attorney Hudson is his first choice to succeed Elsie L. Munsell as federal prosecutor for the Eastern District of Virginia, which stretches from Norfolk to Northern Virginia.

Hudson, whose only known competition for the federal job is Richmond lawyer Richard Cullen, is also said to be favored by U.S. Attorney General Edwin Meese III. It is not clear when the White House will send the nomination to the Senate.

Munsell is not scheduled to vacate the job until early January, and the congressional holiday recess would delay any action on an appointment until Jan. 20 at the earliest.

Three Arlington lawyers have said they want to be commonwealth's attorney if Hudson, a Republican, leaves. The position would be filled by a court appointment until next fall's elections.

Democrats Helen F. Fahey, 44, Hudson's chief deputy, and Brendan Feeley, his opponent in the 1983 election and a former assistant prosecutor, are considered the front-runners for the Arlington job, with Fahey given a slight edge because of her nine years of experience in the office, the last three as second in command.

The only Republican to emerge as a candidate is Liam O'Grady, a 35-year-old assistant prosecutor for three years whose chances are considered slimmer because Democrats and Republicans say they expect a Democrat to get the job, which could pay up to $55,000 a year.

If Hudson leaves his job, Arlington's four Circuit Court judges, themselves elected by the Democrat-controlled state legislature, would name a successor until an election can be held next November to fill the remainder of Hudson's term, which ends in 1987.

The three contenders for the job have deliberately adopted low-key stances, each citing the sensitivity involved in a judicial appointment. Hudson said recently he is avoiding an endorsement because it would be "premature and presumptuous of me to make one." But, he added, he may endorse someone later.

Some Democrats, especially those backing the 38-year-old Feeley, say they hope the court will consider appointing an interim "caretaker" who would not run for office next fall. Such a move would allow Feeley's backers to crank up support among rank and file Democrats for a possible June primary against Fahey. Otherwise, the supporters say, if Fahey is named to the post, she will have a strong edge in any primary.

"There's a lot of sentiment that the Democratic Party owes the job to Brendan Feeley," said one Democratic lawyer, referring to Feeley's willingness to run in 1983 against the popular Hudson, who has run as an independent and attracted substantial support from Democratic voters.

They point to Feeley's experience as a candidate and an assistant prosecutor from 1972 to 1975, and they argue that Fahey has not "paid her dues" to the party.

Those supporting Fahey say length of party activism should not be a criterion for the job she has held longer and more recently than Feeley. They said that, based on her courtroom experience, she would be an able campaigner, and they said that judges have been reluctant to appoint people to offices that they recently sought and lost.

If Feeley or Fahey wins the fall election, Democrats would control every elected local post in the county except for the County Board seat held by Republican Michael E. Brunner.