Cleaves the gamma-glutamyl bond of extracellular glutathione (gamma-Glu-Cys-Gly), glutathione conjugates (such as maresin conjugate (13R)-S-glutathionyl-(14S)-hydroxy-(4Z,7Z,9E,11E,16Z,19Z)- docosahexaenoate, MCTR1) and other gamma-glutamyl compounds (such as leukotriene C4, LTC4) (PubMed:17924658, PubMed:21447318, PubMed:27791009). The metabolism of glutathione by GGT1 releases free glutamate and the dipeptide cysteinyl-glycine, which is hydrolyzed to cysteine and glycine by dipeptidases (PubMed:27791009). In the presence of high concentrations of dipeptides and some amino acids, can also catalyze a transpeptidation reaction, transferring the gamma-glutamyl moiety to an acceptor amino acid to form a new gamma-glutamyl compound (PubMed:17924658, PubMed:21447318, PubMed:7673200, PubMed:7759490, PubMed:8095045, PubMed:8827453). Contributes to cysteine homeostasis, glutathione homeostasis and in the conversion of the leukotriene LTC4 to LTD4. {ECO:0000269|PubMed:17924658, ECO:0000269|PubMed:20622017, ECO:0000269|PubMed:21447318, ECO:0000269|PubMed:24047895, ECO:0000269|PubMed:27791009, ECO:0000269|PubMed:7673200, ECO:0000269|PubMed:7759490, ECO:0000269|PubMed:8095045, ECO:0000269|PubMed:8827453}. [Isoform 3]: Seems to be catalytically inactive. . This is the function of GGT1 (gamma-glutamyltransferase 1, Ensembl gene identifier ENSG00000100031).