When Harry Teter Jr. resigned last week as executive director of the Apalachian Regional Commission, he took along something that has become traditional for parting officials at the poverty agency - a fat consulting contract.

Teter, who was forced out as staff director of the 13-state ARC, will get $35,000 for a six-month review of his years at the commission.

The ARC is a federal-state partnership that has doled out billions of dollars in aid, mostly for highways, health clinics and vocational schools, since 1965. It is run by a triumvirate in Washington, the executive director, a federal co-chairman, and a states' representative for the 13 participating governors.

Practically every high official leaving the ARC has received some kind of consulting fee to help ease the transition from public service.

When John Whisman, longtime states' representative, was pushed out two years ago, he got a $35,000 contract to finance a treatise on his reflections about the ARC.

When Nixon appointee Donald W. Whitehead, the federal co-chairman, made way last summer for a Carter administration successor, he got just under $10,000 to help break in the new man.

Whitehead's predecessors - John L. Sweeney (about $75,000), Joe W. (Pat) Fleming (about $25,000) and John H. Waters Jr. ($6,000) - all took their turns too as consultants when they left the commission.

Some members of the commission's permanent staff have expressed bewilderment, and even a touch of embarrassment, at the ARC's generosity with funds earmarked to help the mountain poor. Some view the consulting contracts as thinly disguised severance pay.

Defenders of the practice, however, say the consulting arrangements are the best way to gain the insights of experienced officials.

The commission's unofficial champion consultant has now joined the agency. After collecting some $300,000 in elegal fees since 1969, Henry Krevor enlisted last year. For now at least he is Teter's replacement.