  We present solutions of DHOST theories describing a rotating black hole
embedded in an expanding universe. The solution is constructed by conformal
transformation of a stealth Kerr(-de Sitter) black hole. The conformal factor
depends explicitly on the scalar field -- but not on its derivative -- and
defines the new theory. The scalar field of the stealth Kerr(-de Sitter)
solution depends on time, leading to the time-dependence of the obtained
conformal metric, with cosmological asymptotics at large distances. We study
the properties of the obtained metric by considering regular null geodesic
congruences, and identify trapping black hole and cosmological horizons.
