Real-time satellite clocks are the basis of real-time precise point positioning (PPP) applications. However, achieving rapid convergence and high-precision clock estimates without relying on external products remains a challenge. In this contribution, a time-differenced carrier phase (TDCP)-assisted multi-GNSS real-time satellite clock estimation method is proposed, in which the satellite clock variations are estimated using the TDCP, so that precise initial clocks can be determined and constrained with appropriate variances in the Kalman filter-based real-time Undifferenced (UD) clock estimation. One week of observations from 66 Multi-GNSS Experiment (MGEX) stations are used to validate the algorithm with the following schemes: the white noise model for Scheme 1 (S1); the proposed method with variances of constraints set to (0.2)2 ns2 (S2), (0.5)2 ns2 (S3), (0.8)2 ns2 (S4), (1.0)2 ns2 (S5). The convergence time and clock precision are found to be significantly improved compared to those of S1, among which S5 shows the best performance. Its convergence time can be improved from 27.0, 33.4, and 21.1 min to 0.6, 0.4, and 0.4 min for GPS, BDS-3, and Galileo satellite clocks, respectively, with improvements of over 97%. The clock precision is improved from 0.187, 0.178, and 0.097 ns applying S1 to 0.041 ns, 0.040 ns, and 0.034 ns, for GPS, BDS-3, and Galileo, respectively, with improvements of over 64%. The improved GNSS clocks also improved the kinematic PPP, i.e., by at least 90% in convergence and 60% in accuracy compared to the white noise model.