Involved in cell wall biogenesis. Has a role in the addition of Gal-beta1,3 moeities to galactomannans and their subsequent pyruvylation. Has a role in meiosis. 3-O-(beta-D-galactosyl-(1->4)-beta-D-xylosyl)-L-seryl-[protein] + UDP-alpha-D-galactose = 3-O-(beta-D-galactosyl-(1->3)-beta-D-galactosyl-(1->4)-beta-D-xylosyl)-L-seryl-[protein] + H(+) + UDP Belongs to the glycosyltransferase 31 family.