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ABSTRACT Understanding the processes that transform star-forming galaxies into quiescent ones is key to unravelling the role of environment in galaxy evolution. We present measurements of the luminosity functions (LFs) and stellar mass functions (SMFs) of passive red-sequence galaxies in four galaxy clusters at $0.8 < z < 1.3$, selected using deep Very Large Telescope (VLT) observations complemented with data from the Gemini CLuster Astrophysics Spectroscopic (GCLASS) and Gemini Observations of Galaxies in Rich Early ENvironments (GOGREEN) surveys. We find a significant enhancement in the abundance of faint/low-mass passive galaxies in both the LFs and SMFs of all four clusters compared to the field. This is further evidenced by a shallower low-mass slope in the composite passive cluster SMF, which yields a Schechter parameter $$\alpha = -0.54^{+\, 0.03}_{-0.03}$$, compared to $$\alpha = 0.12^{+\, 0.01}_{-0.01}$$ for the field. Our findings indicate that quenching processes that act in clusters are enhanced compared to the field, suggesting that environmental quenching mechanisms may already be active by $$z\sim 1$$. To reproduce the observed passive cluster SMF, we estimate that $$25\pm 5~{{\ \rm per\ cent}}$$ of the star-forming field population that falls into the cluster must have been quenched. Our results largely support traditional quenching models but highlight the need for deeper studies of larger cluster samples to better understand the role of environmental quenching in the distant Universe.