High-redshift galaxy clusters, unlike local counterparts, show diverse star formation activities. However, it is still unclear what keeps some of the high-redshift clusters active in star formation. To address this issue, we performed a multiobject spectroscopic observation of 226 high-redshift (0.8<z<1.3) galaxies in galaxy cluster candidates and the areas surrounding them. Our spectroscopic observation reveals six to eight clusters/groups at z~0.9 and z~1.3. The redshift measurements demonstrate the reliability of our photometric redshift measurements, which in turn gives credibility for using photometric redshift members for the analysis of large-scale structures (LSSs). Our investigation of the large-scale environment (~10Mpc) surrounding each galaxy cluster reveals LSSs - structures up to ~10Mpc scale - around many of, but not all, the confirmed overdensities and the cluster candidates. We investigate the correlation between quiescent galaxy fraction of galaxy overdensities and their surrounding LSSs, with a larger sample of ~20 overdensities including photometrically selected overdensities at 0.6<z<0.9. Interestingly, galaxy overdensities embedded within these extended LSSs show a lower fraction of quiescent galaxies (~20 per cent) than isolated ones at similar redshifts (with a quiescent galaxy fraction of ~50 per cent). Furthermore, we find a possible indication that clusters/groups with a high quiescent galaxy fraction are more centrally concentrated. Based on these results, we suggest that LSSs are the main reservoirs of gas and star-forming galaxies to keep galaxy clusters fresh and extended in size at z~1.