[U]ltra-precise clocks can be used to improve synchronization in navigation and positioning systems, telecommunications networks, and wireless and deep-space communications.
The fact of the matter is the one of the most important applications of these clocks is for a national ballistic missile defense. Ballistic missile defense system use the global positioning system (GPS) as a key element at multiple stages of the process -- typically in missile defense systems, GPS is used both to locate the sensor that identifies a missile launch, which in turn is used to identify the direction and speed and location of the incoming missile, and GPS is also used as part of the navigation system for an anti-missile interceptor.
One of the largest sources of inaccuracy in GPS locations is clock accuracy. A raw GPS signal is accurate to about 15 meters, which is then refined with a variety of methods to improve accuracy, the most common of which supplement satellite signals with fairly short range signals that correct the error in the incoming signal based on its difference from a known local position. This brings accuracy to perhaps 1-3 meters of a target. But, in a scenario like a ship based launch detection system far from U.S. controlled territory, it may be difficult to set up that error correction system.
More accurate clocks might improve this level of accuracy by as much as an order of magnitude. And, when the target is a supersonic ballistic missile, the time piece of the calculation may be particularly important. The difference between a +/- 3 meter accuracy and a +/- 300mm accuracy, for example, could easily be the difference between a hit and a miss for a target of that size. And, if the target is a nuclear missile launched from North Korea, that could be the difference between life and death for the residents of some major city in its path, like Seattle, which is believed to be within range of the longest range missiles that North Korea has, if it could get those long range missiles to work (the last test didn't do that, but also provided data to fix its long range missiles for future launches).