Prince George's County Executive Parris N. Glendening's plan to seek state approval for potential new taxes may have already run aground by failing to gain crucial early support from the county's legislative delegation.

Glendening and his advisers have long complained that Prince George's loses millions of dollars by failing to impose a series of taxes that surrounding jurisdictions collect routinely.

But several of the state legislators, who are scheduled to meet with Glendening in College Park tonight to listen to the county executive's latest budget pitch, are complaining that county residents who voted to lift the TRIM property tax revenue cap last month are already paying enough in new taxes.

Although county administration officials said that they have not decided whether they will seek new taxes, they concede that they have been casting about among their supporters to see who would back such a plan.

Democratic Del. Albert Wynn said Glendening approached him earlier this month and told him he would likely be looking at additional tax measures, including a tax on the commercial use of utilities.

"He said we need major enhancements in areas like education," Wynn said. "I agree, and I told him I was generally supportive, but I want to see some numbers."

According to a chart drawn up by the county executive's staff, Prince George's already imposes taxes on admissions and amusements, hotels and motels, recordation, trailer parks and transfer of real estate, all under taxing authority granted by the state.

Other Maryland jurisdictions, including Anne Arundel, Baltimore, Harford, Howard and Montgomery counties as well as the city of Baltimore, have state authority to impose those taxes as well as assessments on utilities, parking and telephone service.

Glendening said last week that he has ruled out a telephone tax and does not think there are enough private parking facilities in the county to raise much money through an assessment on parking lot operators.

He also has said he will shy away from any new taxes that would further burden single-family homeowners. This leaves the option of taxing the commercial users of electricity and fuels.

But Glendening said that it would be "inappropriate" to say what he is angling for yet.

Del. Timothy Maloney, another county Democrat, said the success of the campaign to relax the TRIM property tax limit was no indication that county residents are willing to absorb more taxes.

"TRIM won by 7,000 votes," Maloney said of the modification effort. "That's hardly a mandate."

Any proposal to ask for new taxes, Maloney added, was "dead from the moment the words left Glendening's mouth."

The idea of returning to Annapolis so soon after the TRIM modification to ask for still new ways to collect taxes, said Maloney, who is a member of the House Appropriations Committee, is not sitting well with legislators this year, even if the money is slated to go for education and public safety. "Even that song gets a little tired after a while," he added.

Bowie Democrat Joan Pitkin said that she does not "see a lot of sentiment for raising taxes" within the delegation.

And New Carrollton Democrat Frank B. Pesci said, "I already hear my colleagues privately saying, 'What's the matter with Parris? He can't do that. We're all coming up for reelection in two years.' "

Glendening first appealed to the legislative delegation indirectly, at a briefing held a week ago at the Inglewood Business Park in Landover, where he talked about the county's economic development push.

Instead of imposing new taxes, some lawmakers have said, the administration should be thinking about decreasing the local tax burden.

Pesci and seven other delegates have introduced General Assembly legislation that would repeal a controversial increase in the real estate transfer tax approved by the General Assembly in April and the County Council in June.

That action raised the tax levied on home transfers from 1 percent to 1.5 percent, and it is expected to raise $7.5 million this year, an increase that is scheduled to expire in 1987.

Pesci said that he is willing to amend his bill so that the increase ends in 1986, a year when $16 million in projected additional property tax revenues brought about by the TRIM modification will be available.

Royal Hart, a former state senator who acts as the county's legislative liaison, said that balancing TRIM funds with transfer tax revenues will not work.

"You'd still be giving somebody else a tax break," said Hart, referring to the real estate industry, which opposed the transfer tax increase.

But Pesci said that piecemeal granting of taxing authority is not the solution either. "Nobody wants to put the county to the wall," he said. "But Parris keeps coming up with this Band-Aid approach."

The relaxation of TRIM, according to Glendening, proves that county taxpayers want to maintain government services at a reasonable level.

"The next question is, should we be prepared to start improving services?" he said.

The most improvements, he added, should come in education and public safety, a theme he repeated often during the last TRIM campaign.

"Under a maintenance-type scenario, we're simply not going to be able to make those improvements," Glendening said.