Catalyzes the transfer of Gal to GlcNAc-based acceptors with a preference for the core3 O-linked glycan GlcNAc(beta1,3)GalNAc structure. Can use glycolipid LC3Cer as an efficient acceptor (By similarity). globoside Gb4Cer (d18:1(4E)) + UDP-alpha-D-galactose = globoside GalGb4Cer (d18:1(4E)) + H(+) + UDP Protein modification; protein glycosylation. Belongs to the glycosyltransferase 31 family.