Catalyzes the synthesis of gamma-glutamylcysteine (gamma-GC), the main low-molecular-weight thiol compound instead of glutathione in halophilic archaea. ATP + L-cysteine + L-glutamate = ADP + gamma-L-glutamyl-L-cysteine + H(+) + phosphate Belongs to the glutamate--cysteine ligase type 2 family. YbdK subfamily.