  In this paper, following Nourdin-Peccati's methodology, we combine the
Malliavin calculus and Stein's method to provide general bounds on the
Wasserstein distance between functionals of a compound Hawkes process and a
given Gaussian density. To achieve this, we rely on the Poisson embedding
representation of an Hawkes process to provide a Malliavin calculus for the
Hawkes processes, and more generally for compound Hawkes processes. As an
application, we close a gap in the literature by providing the first
Berry-Ess\'een bounds associated to Central Limit Theorems for the compound
Hawkes process.
