He represented the South Australian House of Assembly seat of Light from 1970 to 1993.

Eastick was elected to the House of Assembly for Light, based on Gawler, in 1970.

Two years later, after Steele Hall resigned as LCL leader, the party elected Eastick as his successor.

Eastick also served as Speaker of the South Australian House of Assembly when his successor as South Australia Liberal leader, David Tonkin, was Premier from 1979 to 1982.

In 1996, Eastick was made a Member of the Order of Australia (AM), in recognition of his "service to the South Australian Parliament, local government and the community".