The Montgomery County Council, seeking to increase its influence in Annapolis, has decided to hire a prominent Democrat as its liaison to the legislature.

The county Contract Review Committee, which oversees all contracts, yesterday approved the selection of Patricia Billings, a top official in the state Democratic Party and legislative aide to Del. Helen Koss (D-Montgomery).

Billings and council staff members are still negotiating her salary for the job, but one official familiar with the discussions said the salary for eight months of work each year will be $20,000 plus $5,000 for expenses. The council is expected to approve the contract next Tuesday.

The council has for many years used a part-time consultant to lobby for local legislation in Annapolis. Billings' job will also officially be part-time but her duties were expanded to include pre-session lobbying.

Billings, 45, chairs the state party's delegate-selection committee for the 1984 Democratic national convention and has long been active in county politics.

Her selection marks the increased emphasis that council members are placing on the lobbying job, which will be particularly crucial during next year's expected debate on changes in state funding for schools and local services, officials said yesterday.

"Her importance will be in assuming the council's interest, rather than the executive's," said council member Neal Potter. "Her job will be to help us make sure that there's not a funding calamity for our school system, our transit system and other programs."

Potter and other officials said the selection of Billings was not intended to reflect dissatisfaction with Blair Lee IV, the legislative lobbyist and cabinet officer hired by County Executive Charles W. Gilchrist in 1979.

Lee, who is known as one of the most effective local government lobbyists, has in the past briefed council members during the legislative season. At the same time, however, the officials said Lee's two-member staff was too small to meet the council's needs.

"Blair frankly doesn't have the resources, the people-power to be responsive to us," said one council staff member who asked not to be named.

Council members and a top Gilchrist aide stressed that the appointment of Billings was not a product of the public rift between the executive and the council's four-member majority. "This is not to create any role for the council against the executive," said Potter, a frequent Gilchrist ally who supports the appointment.

Billings said she expects to work closely with Lee. Billings was one of four applicants for the lobbyist's job. Others included former Del. Robert A. Jacques, a Rockville lawyer, and Steven A. Silverman, a consultant and aide to former delegate Luiz Simmons, a Montgomery Republican, officials said.