Alp14 is a TOG-family microtubule polymerase from S. pombe that tracks plus ends and accelerates their growth. To interrogate its mechanism, we reconstituted dynamically unstable single isoform S. pombe microtubules with full length Alp14/TOG and Alp7, the TACC-family binding partner of Alp14. We find that Alp14 can drive microtubule plus end growth at GTP-tubulin concentrations at least 10-fold below the usual critical concentration, at the expense of increased catastrophe. This reveals Alp14 to be a highly unusual enzyme that biases the equilibrium for the reaction that it catalyses. Alp7/TACC enhances the effectiveness of Alp14, by increasing its occupancy. Consistent with this, we show in live cells that Alp7 deletion produces very similar MT dynamics defects to Alp14 deletion. The ability of Alp7/14 to accelerate and bias GTP-tubulin exchange at microtubule plus ends allows it to generate long-lived, fast-growing microtubules at very low cellular free tubulin concentrations.