Let me presume that Sigma is psd, Let C = chol(Sigma).
Then
trace(Sigma*inv(gama*eye(n)-L)) = trace(C'*C*inv(gama*eye(n)-L)) = trace(C*inv(gama*eye(n)-L)*C') by cyclic permutation invariance of trace.
Now apply my solution approach in Generalizing "trace_inv" for matrix quadratic forms .
Alternatively, use Sigma = sqrtm(Sigma)*sqrtm(Sigma) instead of the Cholesky factorization, which will also handle the case in which the Cholesky factorization does not exist due to (near) singularity.
There are a few other comments by me at How to compute inverse of matrix .