We assess the feasibility of detecting the compact object remnants from Population III (Pop III) stars in nearby dense star clusters, where they become luminous again as X-ray binaries (XRBs) and tidal disruption events (TDEs) via strong tidal encounters. Analytically modelling the formation of Pop III stars, coupled with a top-heavy initial mass function predicted by numerical simulations, we derive the number of (active) Pop III XRBs and TDEs in the present-day Milky Way (MW) nuclear star cluster as โผ 0.06 โ 0.3 and 4 ร 10 โ6 , rendering any detection unlikely. The detection probability, however, can be significantly boosted when surveying all massive star clusters from the MW and neighboring galaxy clusters. Specifically, we predict โผ 1.5 โ 6.5 and โผ 40 โ 2800 active Pop III XRBs in the MW and the Virgo cluster, respectively. Our Pop III XRBs are dominated (โผ 99%) by black holes with a typical mass and luminosity of โผ 45 M and โผ 10 36 erg s โ1 . Deep surveys of nearby ( 30 โ 300 Mpc) galaxy clusters for such Pop III XRBs are well within reach of next-generation X-ray telescopes, such as ATHENA and LYNX.