Cells couple growth with division and regulate size in response to nutrient availability. In rod-shaped fission yeast, cell-size control occurs at mitotic commitment. An important regulator is the DYRK-family kinase Pom1, which forms gradients from cell poles and inhibits the mitotic activator Cdr2, itself localized at the medial cortex. Where and when Pom1 modulates Cdr2 activity is unclear as Pom1 medial cortical levels remain constant during cell elongation. Here we show that Pom1 re-localizes to cell sides upon environmental glucose limitation, where it strongly delays mitosis. This re-localization is caused by severe microtubule destabilization upon glucose starvation, with microtubules undergoing catastrophe and depositing the Pom1 gradient nucleator Tea4 at cell sides. Microtubule destabilization requires PKA/Pka1 activity, which negatively regulates the microtubule rescue factor CLASP/Cls1/Peg1, reducing CLASP's ability to stabilize microtubules. Thus, PKA signalling tunes CLASP's activity to promote Pom1 cell side localization and buffer cell size upon glucose starvation.