A turbine engine assembly includes a first component, a second component and a third component arranged along an axis. The first component houses at least a portion of the third component. The assembly also includes a seal carrier, a seal land and a seal element, which seals a gap between the seal carrier and the seal land. The seal carrier is connected to the first component, and includes a groove surface and a groove. A first portion of the seal carrier seals a gap between a second portion of the seal carrier and the second component. The seal land is connected to the third component and includes a seal land surface. The seal element extends radially into the groove. The seal element is axially engaged with the groove surface and radially engaged with the seal land surface.