The observed correlation between the far-infrared and radio luminosities of galaxies illustrates the close connection between star formation and cosmic-ray production. Intriguingly, recent gamma-ray observations indicate that recycled/millisecond pulsars (MSPs), which do not trace recent star formation, may also efficiently accelerate cosmic-ray electrons. We study the contribution of MSPs to the galactic nonthermal radio emission, finding that they can dominate the emission from massive quiescent galaxies. This model can explain recent LOFAR observations that found a peculiar radio excess in galaxies with high stellar masses and low star-formation rates. We show that MSP-based models provide a significantly improved fit to LOFAR data. We discuss the implications for the radio-far-infrared correlation, the observation of radio excesses in nearby galaxies, and local electron and positron observations.