Detecting Gravitational Waves (GWs) in the 0.1 mHz to 1 Hz range is a crucial step in exploring the longstanding astrophysical mysteries surrounding the coevolution of supermassive black holes at galactic centers and their host galaxies. It is estimated that GWs can only induce spatial changes on the order of 10^-21, which poses a significant challenge for ground-based observatories due to spatial constraints and interference from the ground and atmosphere. Fortunately, space-based GWs observatories can offer promising solutions, where signals are expected to be larger in number and characterized by larger amplitudes. Notable examples include the Laser Interferometer Space Antenna (LISA), Tianqin, and Taiji. All these missions deploy three synchronized satellites in a triangular configuration, separated by arm lengths of 10?~10? meters, forming a colossal interferometer in space. Each satellite houses two free-falling test masses, whose relative displacements are monitored via laser interferometry. By analyzing the movement between these masses with ultra-stable clocks, scientists aim to extract faint GWs buried in noise. The detection of GWs necessitates displacement measurements with an extraordinary precision of tens of picometers. Achieving such precision demands the suppression of noise sources, particularly laser frequency fluctuations, to an extraordinary degree. In addition to optimizing the structure of the interferometer using Pound-Drever-Hall (PDH) frequency stabilization and arm-locking techniques, researchers are now using Time-Delay Interferometer (TDI) techniques to improve the accuracy of gravitational wave detection. TDI represents a computational tour de force: it processes phase data collected from satellites at varying light-travel times and combines them algorithmically to cancel laser frequency fluctuations. For example, differential measurements between satellites are delayed and summed to nullify phase drifts caused by imperfect laser coherence. This approach effectively mitigates noise while preserving GW signatures. A critical subsystem is the timing system. To meet the requirements of GWs detection, phase measurements require clock stability better than 10-15. Traditional atomic clocks meet the stability requirements but are impractical for space missions due to their size, weight, and power consumption. In contrast, quartz clocks offer advantages in size and weight but fall short in stability. Under this circumstance, improving the clock's stability while optimizing its size and structure has become a critical challenge to address. The optical frequency comb-based TDI (OFC-TDI) technique was proposed to simplify the difficulty. OFCs generate ultra-stable, evenly spaced spectral lines across a broad frequency range. OFC-TDI technique uses the repetition frequency of the OFC as the clock for the heterodyne measurements, allowing phase fluctuations to be coherently transferred to microwave signals through its broad spectral characteristics. This approach directly eliminates laser noise, significantly simplifying the system structure and reducing the likelihood of subsystem failures. Recent advancements in miniaturizing mode-locked lasers, the core components of OFCs, have accelerated the development of compact, space-qualified systems. Compared to fiber lasers, solid-state lasers provide superior beam quality and longer lifetime. This paper presents an integrated Kerr lens-locked laser based on an irradiation-resistant Yb∶Y₂O₃ ceramic for the low-noise clock. The laser is fully integrated into a compact volume of 61 mL. By optimizing the pump structure, all optical components of the laser are confined to an area of 34×78 mm², which allows for precise temperature control. The temperature control helps the laser achieve a timing jitter of 28 fs. The low power consumption of the laser is only 4 W. The small size, low noise, low power consumption, and long lifetime make the integrated ceramic laser as an ideal tool for gravitational wave detection. In addition, the laser operates near a center wavelength of 1 076.5 nm with a spectral width of 8.58 nm. The relative power stability of the laser is within 0.4% over a two-hour period.