The Washington Post registered major gains in circulation in the wake of the closing of The Washington Star, according to figures released by the newspaper company yesterday.

Since The Star closed, Washington Post daily circulation rose from 595,953 to 730,003 as of Sept. 30--an increase of 22.3 percent. Sunday circulation climbed by 15 percent from 827,620 to 952,539 as of Sept. 30.

The Sept. 30 daily circulation figure was also 25 percent higher than daily circulation a year before. Sunday circulation was up 16 percent from a year earlier. The circulation figures come from statistics filed with the Audit Bureau of Circulation and are subject to audit.

According to The Washington Post's vice president for circulation, Joseph J. Haraburda, the newspaper's circulation has been substantially higher than previous year's levels all year long, including in the period before The Star closed on Aug. 8. But he added that the shutdown of the metropolitan area's other daily obviously had a substantial impact.

While producing a circulation bonanza for The Washington Post, The Star closing also produced problems for The Post in servicing new readers. "We had problems to deal with producing the papers here at The Post and getting them out to distributors," said Haraburda. That problem has been alleviated by the opening of The Post's southeast plant at The Star's former building, he said.

He also said that distributors and deliverers had problems processing large numbers of new orders, which numbered as high as 7,000 a day at least once. Now new orders have leveled off to a more typical level of 1,000 a day, he said.

Figures reported March 31, before The Star closed, showed Post daily circulation at 618,111 and Sunday circulation at 845,176. The figures released yesterday were up 19 percent and 13 percent from those levels.

The figures indicate that Post circulation declined somewhat from March 31 (the date of the last audited figures) to the day before The Star folded. Haraburda said that slight decline reflected a seasonal pattern and noted that Post circulation in July was higher by approximately 15,000 readers daily and about 7,000 Sunday than it had been in July 1980.