After years of negotiation and with the help of Arnold Palmer, the prince George's County government and the Prince George's Country Club have worked out an arrangement to provide a new public park for inner-Beltway residents near Landover and a championship golf course in a posh setting to attract new life into the 57-year-old private club.

In a complicated agreement approved by the County Council and stockholders of the Prince George's Country Club last week, the county agreed to sell 218 acres of land at Woodmore and Enterprise roads in Mitchellville to Golf American Corp., which already owns approximately 700 acres surrounding the Mitchellville site.

Golf American then will trade the 218 acres for 153 acres owned by the country club near Landover and agree to design the country club and golf course on the Mitchellville site. The Maryland National Park and Planning Commission, acting for the county, will buy the Landover golf course from Golf America for $3.2 million.

The county has long been anxious to secure land in the highly developed area of Palmer Park-Cheverly and Landover for a public park. The county saw the Golf America arrangement as a way to do that, according to council sources.

Golf American would build on its 700 acres in Mitchellville 450 luxury-priced houses around the country club's Arnold Palmer designed golf course.

For officials eager to attract upper-income businessmen to the county, the Palmer name and the villa-type development is looked upon as a major incentive for the prince George's County Club-county agreement.

The county plans to lease the Landover country club land for two years back to the Prince George's Country Club while construction on the new development in Mitchellville begins. The county plans to make available some use of the swimming pool, tennis courts and other activities at the club to the public during that time.

Kenneth H. Michael, member of the P.G.C.C. and broker of the land sale, said, "the membership could raise holy heck over (public use) should it infringe upon the golfing facilities."

But Michael added, "The Board of Directors of the club could override any opposition to the plan."

At a county council committee of the whole meeting last week, Michael said public use of the golf club facilities was a "sensitive area" but would be worked out in a joint meeting with the park and planning commission.

Funds for the county purchase would come from state open space grants, the county's advance land acquisition fund and capital projects deleted from this year's budget. The county also anticipates selling 38 acres of the Landover club land for industrial use.

"We want this whole thing to pay for itself," council member David Hartlove told the council.