Zinc phosphodiesterase, which displays tRNA 3'-processing endonuclease activity. Involved in tRNA maturation, by removing a 3'-trailer from precursor tRNA. Can process the mitochondrial tRNA-like structures (t-elements). Endonucleolytic cleavage of RNA, removing extra 3' nucleotides from tRNA precursor, generating 3' termini of tRNAs. A 3'-hydroxy group is left at the tRNA terminus and a 5'-phosphoryl group is left at the trailer molecule. Homodimer. No visible phenotype due to the redundancy with TRZ3. Trz3 and trz4 double mutants are lethal. Belongs to the RNase Z family.