Galaxy clusters are large gravitationally bound, extremely over-dense regions of the universe, and as such they therefore provide interesting conditions that affect the average properties of galaxies, such as star formation activity and star formation history. Galaxy spectra are effective tools for measuring environmental properties. Here, we present an analysis comparing two observables; 1) The 4000-angstrom break (Dn4000), which gives information on the saturation of older or younger stars in each galaxy measured from the flux ratio redward and blueward of 4000 angstroms and 2) The product of the normalized peculiar velocity and the normalized projected radius of each cluster galaxy - this quantity reflects the observable phase-space properties of cluster member galaxies, and serves as a proxy for how recently each galaxy became gravitationally bound to its cluster. Working with a data set of a spectroscopic follow-up of >3000 galaxies in 100 galaxy clusters collected from the Sunyaev Zel’dovich selected galaxy clusters from the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT), we looked at trends in redshift, the location of galaxies in their respective clusters, Dn4000, and a formulated in-fall proxy. Splitting up the galaxies into three redshift bins spanning from ~0.3 to 1, we averaged the Dn4000 values to find two results. First, we saw a trend between Dn4000 and the in-fall proxy where Dn4000 decreases in more recently in-fallen galaxies, implying clusters consistently “shut-down” star formation within galaxies that are in clusters. Secondly, we saw the same qualitative trends between Dn4000 and in-fall time at all redshifts, but the average Dn4000 of cluster galaxies also decrease universally with revealing that star-formation has generally decreased in galaxy clusters since a redshift of ~1.