The use of Global Navigation Satellite System (GNSS) observations collected onboard Low Earth Orbit (LEO) satellites to enhance GNSS satellite precise orbit determination has been intensively investigated. The fast speeds of LEO satellites deliver rapid geometry changes, which are beneficial for improving the GNSS satellite orbital accuracy. Their uniform distribution around the Earth can cover oceans, deserts, and other remote areas that make it difficult to build ground stations. In this contribution, the focus is on real-time GNSS satellite clock estimation (SCE) by integrating GNSS observations collected from regional ground stations and onboard LEO satellites. The proposed method is validated using three designed schemes, namely multi-GNSS real-time SCE using 1) 5 European regional stations (defined as S1); 2) 5 European regional stations and simulated observations of 60 LEO satellites, with the LEO satellite orbits/clocks assumed as known (S2); and 3) 65 globally distributed stations (S3). The GNSS SCE is initiated every 4 h. Results show that the availability of S1, S2, and S3 is about 34%, 100%, and 100%, respectively. Compared to S3, the convergence time of the proposed S2 is significantly shortened from 25.5, 29.7, and 19.1 min to 15.7, 18.2, and 12.9 min for GPS, BDS-3, and Galileo, with improvements of 38.4%, 38.7%, and 32.5%, respectively. The clock precision, i.e., the standard deviations of the clock errors, of 4-hourly solutions amounts to 0.157, 0.153, and 0.080 ns for GPS, BDS-3, and Galileo in S3, respectively, and are improved to 0.048, 0.061, and 0.036 ns applying S2, with improvements of 69.4%, 60.1%, and 55.0%. The GNSS satellite clock estimates are validated by the kinematic precise point positioning tests. Using the 4-hourly estimated clock, compared to S3, the positioning accuracy using S2 is improved from 6.2, 5.1, and 7.9 cm for the East, North, and Up components to 3.8, 3.1, and 4.6 cm, respectively. It is anticipated that integrating regional ground stations and LEO onboard observations can reduce the dependence on full-time and real-time GNSS SCE from global ground stations. It outperforms the ground-station-only GNSS SCE approach in both the convergence time and precision.