Urs Schreiber has written a lot
on gerbes and their applications to physics:
https://ncatlab.org/nlab/show/Urs+Schreiber

See, for instance, the expository works
“Differential cohomology in a cohesive ∞-topos”
and “Higher prequantum geometry”.
Most of his published papers (https://arxiv.org/find/math/1/au:+Schreiber_U/0/1/0/all/0/1) use gerbes in some way.

Almost all of [Konrad Waldorf's papers](http://math.konradwaldorf.de/www/?show=papers&lg=en) also involve gerbes in some way,
and some of them may be more accessible to a beginner,
see, e.g., his survey with Christoph Schweigert [Gerbes and Lie Groups](https://arxiv.org/abs/0710.5467).