As of jamming most probably the new clock will not help. But for spoofing it probably can be prevented and mitigated with the new clock, but the root cause is the pseudo-orthogonality of the spread spectrum.
To put it simply, in housing property market the main criteria are three namely location, location, location. Similarly in communication and specifically in wireless the main criteria are also three namely orthogonality, orthogonality, orthogonality.
It's interesting to note that all mainstream GNSS systems including GPS, Galileo, GLONASS, and BeiDou are using spread spectrum modulation system, and they all affected by the pseudo-orthogonality of the spread spectrum system. There's a reason why the newer 4G/5G, and even Wi-Fi have moved away from spread spectrum modulation that's was being initially used by 3G and 802.11b, respectively, by fully embracing OFDM. The reverse-engineered Starlink modulation is reportedly using OFDM as well [1]. This mainly because of spread spectrum limitations but at the time it's not due to spoofing (security) but due to bandwidth scaling (performance) limitations. For GNSS on the other hand, don't care about the bandwidth because it's for location service not streaming video, but the limitations of being pseudo-orthogonal eventually got to them in the form of spoofing vulnerability.
The next generation GNSS designers perhaps need to bite the bullet, and should employ proper orthogonal modulation (OFDM or others), not pseudo one like spread spectrum. Having highly accurate on board clock is a hacked solution at best, not a proper solution, and it just unnecessarily increase the upfront cost and maintenance complexity by being overkill and over engineered.
[1] Reverse Engineered Signal Structure of the Starlink Ku-Band Downlink (2022) [PDF]:
https://radionavlab.ae.utexas.edu/wp-content/uploads/starlin...