Cysteine protease that plays a key role in autophagy by mediating both proteolytic activation and delipidation of ATG8 family proteins (By similarity). The protease activity is required for proteolytic activation of ATG8 family proteins to reveal a C-terminal glycine (By similarity). Exposure of the glycine at the C-terminus is essential for ATG8 proteins conjugation to phosphatidylethanolamine (PE) and insertion to membranes, which is necessary for autophagy (By similarity). In addition to the protease activity, also mediates delipidation of ATG8 family proteins. Catalyzes delipidation of PE-conjugated forms of ATG8 proteins during macroautophagy (By similarity). Also involved in non-canonical autophagy, a parallel pathway involving conjugation of ATG8 proteins to single membranes at endolysosomal compartments, by catalyzing delipidation of ATG8 proteins conjugated to phosphatidylserine (PS) (By similarity). ATG4D plays a role in the autophagy-mediated neuronal homeostasis in the central nervous system (PubMed:25875846). [protein]-C-terminal L-amino acid-glycyl-phosphatidylethanolamide + H2O = [protein]-C-terminal L-amino acid-glycine + a 1,2-diacyl-sn-glycero-3-phosphoethanolamine [protein]-C-terminal L-amino acid-glycyl-phosphatidylserine + H2O = [protein]-C-terminal L-amino acid-glycine + a 1,2-diacyl-sn-glycero-3-phospho-L-serine Morpholino knockdown of the protein results in neurodegeneration in the central nervous system (CNS) (PubMed:25875846). Neurodegeneration is characterized by severe visible malformations in the developing CNS in regions that correspond to the midbrain-hindbrain boundary, the cerebellum and the hindbrain region (PubMed:25875846). Belongs to the peptidase C54 family.