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) Component of a yeast aminoacyl-tRNA synthase (aaRS) complex formed by methionyl-tRNA synthase, glutamyl-tRNA synthase and the tRNA aminoacylation cofactor arc1 in a stoichiometric complex. Interacts with arc1/SPAC30C2.04 (By similarity). Belongs to the class-I aminoacyl-tRNA synthetase family. Glutamate--tRNA ligase type 2 subfamily.