Is there an improved Pershing on the way?
No real need. Current cruise missile technology is often a better if slower answer - as the Russians have been paying considerable attention and money to ABM defense.
The AGM-158B JASSM-ER already has a powered range of over 570 miles with a 1000lb payload; it’s a stealthy subsonic cruise missile that’s already in service. As of September 2018, Lockheed has been contracted to build a JASSM-XR - an “extreme range” version that can carry a 2000lb warhead out to 1200 miles.
The Pershing II could only throw about 1000lbs out to about 1100 miles and it was blindingly obvious when you launched one. Short flight time could be an advantage, but in a first strike all that a Pershing does before it gets to its destination is give the other guy notice and let him get off return fire.