Metallocarboxypeptidase that mediates protein deglutamylation of tubulin and non-tubulin target proteins. Catalyzes the removal of polyglutamate side chains present on the gamma-carboxyl group of glutamate residues within the C-terminal tail of tubulin protein. Specifically cleaves tubulin long-side-chains, while it is not able to remove the branching point glutamate. Also catalyzes the removal of polyglutamate residues from the carboxy-terminus of non-tubulin proteins such as MYLK. Mediates the deglutamylation of nucleotidyltransferase CGAS, leading to CGAS antiviral defense response activation (By similarity). Involved in KLF4 deglutamylation which promotes KLF4 proteasome-mediated degradation, thereby negatively regulating cell pluripotency maintenance and embryogenesis (PubMed:29593216). {ECO:0000250|UniProtKB:Q09LZ8, ECO:0000269|PubMed:29593216}. This is the function of Ensembl gene identifier ENSG00000186094 (AGBL4, AGBL carboxypeptidase 4).