Using a sample of $1.06times10^8 psip$ events produced in $e^+e^-$ collisions at $sqrt{s}$ = 3.686 GeV and collected with the BESIII detector at the BEPCII collider, we present studies of the decays $klx+c.c.$ and $gklx+c.c.$. We observe two hyperons, $Xi(1690)^-$ and $Xi(1820)^-$, in the $K^-Lambda$ invariant mass distribution in the decay $klx+c.c.$ with significances of $4.9 sigma$ and $6.2 sigma$, respectively. The branching fractions of $klx+c.c.$, $ksx+c.c.$, $psiptogamma chi_{cJ}to gamma K^- Lambda bar{Xi}^+ +c.c.$ $(J=0, 1, 2)$, and $psipto Xi(1690/1820)^{-} bar{Xi}^++c.c$ with subsequent decay $Xi(1690/1820)^-to K^-Lambda$ are measured for the first time.