Cysteine protease that plays a key role in cytoplasm to vacuole transport (Cvt) and autophagy by mediating both proteolytic activation and delipidation of ATG8 (PubMed:26442587). Required for selective autophagic degradation of the nucleus (nucleophagy) as well as for mitophagy which contributes to regulate mitochondrial quantity and quality by eliminating the mitochondria to a basal level to fulfill cellular energy requirements and preventing excess ROS production (By similarity). The protease activity is required for proteolytic activation of ATG8: cleaves the C-terminal amino acid of ATG8 to reveal a C-terminal glycine (PubMed:26442587). ATG8 ubiquitin-like activity requires the exposure of the glycine at the C-terminus for its conjugation to phosphatidylethanolamine (PE) and its insertion to membranes, which is necessary for autophagy (PubMed:26442587). The ATG8-PE conjugate mediates tethering between adjacent membranes and stimulates membrane hemifusion, leading to expansion of the autophagosomal membrane during autophagy. In addition to the protease activity, also catalyzes deconjugation of PE-conjugated forms of ATG8 during macroautophagy: ATG8 delipidation is required to release the protein from membranes, which facilitates multiple events during macroautophagy, and especially for efficient autophagosome biogenesis, the assembly of ATG9-containing tubulovesicular clusters into phagophores/autophagosomes, and for the disassembly of PAS-associated ATG components. ATG8 delipidation by ATG4 also recycles ATG8-PE generated on inappropriate membranes to maintain a reservoir of unlipidated ATG8 that is required for autophagosome formation at the PAS (By similarity). [protein]-C-terminal L-amino acid-glycyl-phosphatidylethanolamide + H2O = [protein]-C-terminal L-amino acid-glycine + a 1,2-diacyl-sn-glycero-3-phosphoethanolamine Interacts with ATG8 (By similarity). Impairs the formation of preautophagosomal structures (PubMed:26442587). Blocks the maturation and subsequent localization of ATG8 to autophagic membranes (PubMed:26442587). Kluyveromyces marxianus proteins are shorter in length and have a more ordered secondary structure than their S.cerevisiae counterparts, which might contribute to the superior thermotolerance and solubility (PubMed:26442587). K.marxianus could be therefore useful as a new model organism for further elucidation of the molecular details of autophagy (PubMed:26442587). Belongs to the peptidase C54 family.