  L\'evy copulas are an important tool which can be used to build dependent
L\'evy processes. In a classical setting, they have been used to model
financial applications. In a Bayesian framework they have been employed to
introduce dependent nonparametric priors which allow to model heterogeneous
data. This paper focuses on introducing a new class of L\'evy copulas based on
a class of subordinators recently appeared in the literature, called
\textit{Compound Random Measures}. The well-known Clayton L\'evy copula is a
special case of this new class. Furthermore, we provide some novel results
about the underlying vector of subordinators such as a series representation
and relevant moments. The article concludes with an application to a Danish
fire dataset.
