The TranStab project (3-year duration) associates two academic laboratories (LPL/CNRS UMR 7538/USPN and Institut Foton/CNRS UMR 6082/ENSSAT/Univ. Rennes) and one industrial company (Thales TRT). The project involves the design and realization of compact devices for transferring the stability of a 1.5 µm optical frequency reference (REFIMEVE or a stand-alone reference developed in the ANR ASTRID BRIOCHE project) to wavelengths of interest ranging from the mid-infrared to the visible. Various solutions will be explored: ring cavities for 10-15 level transfer around 1.5 µm with quasi-continuous C+L band coverage, ring cavities with 1.5 µm /1 µm multiplexer coupler for extended transfer towards 1 µm, unbalanced Mach-Zehnder interferometer for transfer up to 980 nm, the operating limit of single-mode fibers. Using non-linear optics techniques, the stability of the 1.5 µm reference will be transposed to sources emitting at the wavelengths of use, in both the IR and visible ranges. Their frequency stability will be metrologically characterized. These sources will enable a variety of high-sensitivity experiments for the realization of sensors and for applications in the field of quantum technologies, representative of the community's needs. The approach adopted in the TranStab project will thus be demonstrated on a variety of applications requiring stability at various wavelengths: high-sensitivity sensors based on Brillouin lasers at 1.5 µm, optical gyroscopes at 633 nm, spectral analysis exploiting the optical coherence properties of Tm3+ ions at cryogenic temperature at 793 nm, addressing of Pr3+ ions at 606 nm for the realization of quantum memories.