The Prince George's County Council yesterday elected as its new chairman Parris N. Glendening, a second-term Democrat from University Park who in the last year has emerged as Republican County Executive Lawrence Hogan's most vocal and persistent critic.

Glendening 37, a political science professor at the University of Maryland, who openly aspires to replace Hogan in 1982, was elected by a unanimous vote of his 10 Democratic colleagues.

He will assume the position when the council begins its new session Tuesday.

Glendening and Hogan have not spoken to each other since August, when Hogan verbally attacked Glendening at a convention in Ocean City and threatened to publicly embarrass him. The argument followed months of policy disputes between Hogan and the council, ranging from county development personnel issues.

Since then Hogan and Glendening have attempted to tone down their criticism of each other, and yesterday Glendening said he did not expect the past public confrontations to reoccur this year.

"I think everyone realizes that the political differences must be set aside and the functions of government must go on," Glendening said.

Hogan, who has labeled Glendening "overly ambitious" and "untrustworthy," said little yesterday about Glendening's election to chairman.

"Life is not supposed to be a bed of roses," he said.

However, one council official said that Hogan and some of his staff tried to convince council members that Glendening's election would further strain relations between the council and Hogan.

" hogan was more complaining about what he knew was fait accompli [Glendening's election] than trying to lobby anyone," one council member said. "I think he knew a long time ago that it was going to be Paris, whether he wanted it or not."

Glendening's election to chairman had largely been assured a year ago when he unsuccessfully sought the post.

At that time, several council members opposed Glendening's election because they felt he was too openly ambitons. Instead, William B. Amonett was elected as a compromise candidate, and council leaders indicated they would support Glendening this year.

Council members yesterday said they did not think Glendening's election would alter relations between the council and Hogan.

" hogan has created his own problems," said outgoing chairman Amonett. "I don't think anyone doubts that Glendening is the best choice to represent the entire council this year."

The council also elected first-term council member Ann Lombardi, 43, be vice chairman.