Given Kyber crystals are used to make the Death Star laser in A New Hope, Return of the Jedi and I am guessing The Force Awakens and they are also a necessary constituent of a Jedi's lightsaber, is there now a shortage of Kyber crystals in the Galaxy?
I wouldn't use the word "shortage" but something more in the way of "monopoly".
Why ? Because like JBH said in his answer, Kyber crytals were already rare in the Star Wars universe, add to the equation that each reigning power in the galaxy claimed exclusive rights of those and you obtain something rare, hard to come across but not impossible to obtain.
Be it during the time of the Republic :
Over the centuries, the Jedi amassed an almost exclusive right to the crystals, protecting and collecting them to decorate their temples and power their lightsabers.
During the Empire :
Sometime after the fall of the Jedi Order and the Galactic Republic, its successor state—the Galactic Empire—occupied Jedha in order to mine its kyber crystal deposits. Unknown to all but the most high-ranking officials in the Empire, the crystals were being used as components in the construction of an Imperial superlaser capable of destroying entire planets.
And even by the last in date, the First Order :
A shortage can only be declared in context of supply and demand. A material can be quite rare and yet, due to limited demand, not be in a state of "shortage."
From a story-telling POV, Kyber wants to be a fairly rare element. It won't be found on just any old planet. Were it common, every Tom, Dick, and Clone 99 would be building their own lightsabers. They'd be available on every street corner. So, is there a shortage? I don't know. Are they rare? Absolutely. Would that make them hard to come by? Yup.