Summary: The current work applies some recent combinatorial tools due to Jain to control the eigenvalue gaps of a matrix \(M_n = M + N_n\) where \(M\) is deterministic, symmetric with large operator norm and \(N_n\) is a random symmetric matrix with subgaussian entries. One consequence of our tail bounds is that \(M_n\) has simple spectrum with probability at least \(1 - \exp(-n^{2/15})\) which improves on a result of Nguyen, Tao and Vu in terms of both the probability and the size of the matrix \(M\).