Polyglutamylase which modifies tubulin, generating polyglutamate side chains of variable lengths on the gamma-carboxyl group of specific glutamate residues within the C-terminal tail of tubulin. Mediates ATP-dependent polyglutamate side-chain elongation of the polyglutamylation reaction but not the initiation step. Preferentially modifies the alpha-tubulin tail over a beta-tail.
