Question

In between the core of a nutron star and the outer layer, what might the conditions be like.

Answer 1

Well, very high gravity and density, of course, and typically extremely high magnetic fields and temperature. Hard to know what interests you.

Maybe the answer you want is that between the nuclear soup of the interior and the ordinary matter at the edge, there is probably a layer of what's sometimes called degenerate matter, and which makes up most of a white dwarf. This is essentially a sea of electrons in which the nuclei are "dissolved," more or less just like an ordinary metal, only with any element at all -- that is, even hydrogen and helium act like metals under these conditions.

Answer 2

the conditions would likely be....hot