As a star evolves, the orbital distance where liquid water is possible on the surface of an Earth-like planet, the habitable zone, evolves as well. While stellar properties are relatively stable on the main sequence, post-main sequence evolution of a star involves significant changes in stellar temperature and radius, which is reflected in the changing irradiation at a specific orbital distance when the star becomes a red giant, and then later a white dwarf. To search planets in these systems for signs of life it is essential that we understand how stellar evolution influences atmospheric photochemistry along with detectable biosignatures. We use EXO-Prime, which consists of a 1D coupled climate/photochemistry and a line-by-line radiative transfer code, to model the atmospheres and spectra of habitable zone planets around red giants and white dwarfs, and assess the time dependency of detectable biosignatures.