A turbine component assembly is disclosed, including a first component, a second component, and a circumferentially oriented flat spring. The first component is arranged to be disposed adjacent to a hot gas path, and includes a ceramic matrix composite composition. The second component is adjacent to the first component and arranged to be disposed distal from the hot gas path across the first component. The circumferentially oriented flat spring is disposed on and directly contacting the second component and directly contacting and supporting the first component as a compliant contact interface between the first component and the second component. The circumferentially oriented flat spring provides a radial spring compliance between the first component and the second component.