We present the development of a transportable laser frequency stabilization system with application to both optical clocks and a next-generation gravity mission (NGGM) in space. This effort leverages a 5-cm long cubic cavity with crystalline coatings operating at room temperature and with a center wavelength of 1064 nm. The cavity is integrated in a custom vacuum chamber with dedicated low-noise locking electronics. Our vacuum-mounted cavity and control system are well suited for space applications, exhibiting state-of-the-art noise performance while being resilient to radiation exposure, vibration, shock, and temperature variations. Furthermore, we demonstrate a robust means of automatically (re)locking the laser to the cavity when resonance is lost. We show that the mounted cavity is capable of reaching technology readiness level (TRL) 6, paving the way for high-performance ultrastable laser systems and eventually optical atomic clocks amenable to future satellite platforms.