The imminent arrival at the Pentagon of a three-star admiral with close ties to Texas Gov. William P. Clements is sending a new shiver of intrigue to figure out who is up and who is down in the transition to a new administration.

At the request of Clements, the Defense Department, according to informed sources, agreed to transfer Vice Adm. Kenneth M. Carr from his post at Offutt Air Force Base in Nevada into a temporary office specially set up for him on the Pentagon's top-level E-ring.

Carr's mission, these sources said, appears to be one in which he pursues in detail some questions Clements raised in a private meeting at the Pentagon last week with outgoing Secretary of Defense Harold Brown. Those questions are said to involve a survey of military weapon system projects to see which ones would be best suited to speeding up when the new administration takes office.

Administration officials say they assumed that Clements was acting in his role as a member of the high-level interim foreign policy board appointed by Reagan soon after his election and that Clements was operating as Reagan's emissary on this particular matter.

What was most surprising yesterday around the Pentagon, however, was that Carr's transfer here was not made known by Clements to William Van Cleave, the chief of the 13-man Reagan transition team working inside the Pentagon.

Clements served as deputy secretary of defense for four years during the Nixon and Ford administrations and has retained his strong interest in military matters since becoming Texas' first Republican governor two years ago. During those years at the Pentagon, Carr served as Clements' military assistant. Since then, Carr has been vice director of strategic targeting on the joint military staff of the Air Force's Strategic Air Command headquarters in Nebraska.

Officials said the Clements-Carr contacts with the Pentagon have been handled in a very low-key manner, which is apparently what Clements wanted, and that there was considerable interest among senior bureaucrats about just what the admiral was supposed to do and what it meant for the recommendations of the working team headed by Van Cleave.

Some transition team sources said that the admiral's assignment seemed to be the type of thing the transition team would normally do, though they were reluctant to draw any conclusions as to whether it spelled trouble for Van Cleave because they, too, hadn't been told about Carr and thus weren't sure what he was supposed to do.

Van Cleave, a director of the Defense and Strategic Studies Program at the University of Southern California, was the senior defense adviser to Reagan during the campaign. He has strong views on defense, believing the United States must move quickly to patch up certain vulnerabilities even if the cost is high. He is also somewhat controversial within the Reagan camp because he is outspoken on some of these costly issues and is known to be hoping that a Reagan administration will not stray very far from the tough platform that the Republican Party adopted on defense.

There is also interest in the Pentagon transition team because it includes four men who work for defense contractors.

One of them, Ben Plymale, deputy director of the team, is at the same time a top official at Boeing. Government officials say they cannot remember any defense industry persons being involved in at least the last two administration changeover teams. Plymale's case has been called to the attention of the White House and the Reagan staff. Transition sources, however, say there is nothing illegal or improper in this situation.

On the other hand, the transition team did drop Rep. Robin L. Beard (R-Tenn.) after administration concern was expressed about blurring the constitutional separation between legislative and executive branches.