Based on the data sample of $448.1times10^{6}$ $psi(3686)$ events collected with the BESIII detector at BEPCII, we present a study of the decays $psi(3686)rightarrowgammachi_{cJ}rightarrowgammabar{p}K^{*+}Lambda+c.c.$ and $psi(3686)rightarrowbar{p}K^{*+}Lambda+c.c.$. The branching fractions of $chi_{cJ}rightarrowbar{p}K^{*+}Lambda+c.c.$ ($J$=0, 1, 2) are measured to be $(4.8pm0.7pm0.5)times10^{-4}$, $(5.0pm0.5pm0.4)times10^{-4}$, and $(8.2pm0.9pm0.7)times10^{-4}$, respectively, where the first uncertainties are statistical and the second systematic. The branching fraction of $psi(3686)rightarrowbar{p}K^{*+}Lambda+c.c.$ is measured to be $(6.3pm0.5pm0.5)times10^{-5}$. All these decay modes are observed for the first time.