Dating sites and finds is the backbone of archaeology.Regarding Göbekli Tepe, we get lots and lots of questions about its chronology.
Göbekli Tepe was abandoned after the middle PPN B, i.e. That is the time when agriculture finally is fully established; the demise of a hunter-gatherer site would thus fit in this general picture.
There are neither domesticated plants, nor animals at Göbekli Tepe.
These questions are absolutely legitimate (as actually really most of them are), and even more so with a site that claims to be the ‘first’ or ‘oldest’ (yet known) in many respects, the accuracy of dating becomes paramount.
Of course we have a larger number of scientific publications on the topic, and more are under way as we type this.
Layer III, the lower and thus older layer, has the famous circular enclosures with the T-shaped pillars.