Based on the data sample of $448.1 imes10^6$ $psi(3686)$ events collected with the BESIII detector at BEPCII, we present a study of the decays $psi(3686) ightarrowgammachi_cJ ightarrowgammaarpK^*+Lambda+c.c.$ and $psi(3686) ightarrowarpK^*+Lambda+c.c.$. The branching fractions of $chi_cJ ightarrowarpK^*+Lambda+c.c.$ ($J$=0, 1, 2) are measured to be $(4.8pm0.7pm0.5) imes10^-4$, $(5.0pm0.5pm0.4) imes10^-4$, and $(8.2pm0.9pm0.7) imes10^-4$, respectively, where the first uncertainties are statistical and the second systematic. The branching fraction of $psi(3686) ightarrowarpK^*+Lambda+c.c.$ is measured to be $(6.3pm0.5pm0.5) imes10^-5$. All these decay modes are observed for the first time.
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