Optical clocks based on strontium (Sr) atoms and ions are currently used to provide precise standards for measuring time. These devices require several narrow-band visible laser sources at specific wavelengths to operate. We report on the diode-pumped continuous-wave laser operation at 674, 688, 689, 698, and 707 nm of a single crystal of Pr3+:LiGdF4 (Pr:GLF). To the best of our knowledge, Pr:GLF is the only active medium suitable for solid-state laser operation at all the wavelengths of interest for Sr-based clocks in the deep-red region. We also investigated the spectral tunability of this source, achieving an uninterrupted tuning range of 17 nm, between 697 and 714 nm.