This paper investigates charge transport in tunnel junctions based on the two-dimensional magnetic insulator chromium trichloride (CrCl₃). The tunneling device, consisting of a 9 nm thick CrCl3 flake sandwiched between graphite  contacts, exhibited two distinct tunneling mechanisms: direct tunneling at low voltages and Fowler − Nordheim tunneling at high voltages. At low temperatures, tunneling was suppressed by antiparallel spin alignment in CrCl3 layers,  while at high temperatures above 18 K the effective tunnel barrier height decreased and sharp current increase was observed. An unusual increase in the barrier height was observed in the temperature range of 20–23 K. Obtained  results highlight the enhanced spin filtering effects in thicker CrCl₃-based tunnel junctions, providing insights for spintronic applications.