Catalyzes the attachment of glutamate to tRNA(Glu) in a two-step reaction: glutamate is first activated by ATP to form Glu-AMP and then transferred to the acceptor end of tRNA(Glu). ATP + L-glutamate + tRNA(Glu) = AMP + diphosphate + L-glutamyl-tRNA(Glu) Binds 1 zinc ion per subunit. Monomer. Belongs to the class-I aminoacyl-tRNA synthetase family. Glutamate--tRNA ligase type 1 subfamily.