Catalyzes the tRNA-independent activation of glutamate in presence of ATP and the subsequent transfer of glutamate onto tRNA(Asp). Glutamate is transferred on the 2-amino-5-(4,5-dihydroxy-2-cyclopenten-1-yl) moiety of the queuosine in position 34 of the tRNA(Asp), the wobble position of the QUC anticodon. Does not transfer glutamate to either tRNA(Glu) or tRNA(Gln). The incapacity of the glutamylated tRNA(Asp) to bind elongation factor Tu suggests that it is not involved in ribosomal protein biosynthesis. Binds 1 zinc ion per subunit. Belongs to the class-I aminoacyl-tRNA synthetase family. GluQ subfamily.