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 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.