  We consider the notion of equivariant uniform property Gamma for actions of
countable discrete groups on C*-algebras that admit traces. In case the group
is amenable and the C*-algebra has a compact tracial state space, we prove that
this property implies a kind of tracial local-to-global principle for the
C*-dynamical system, generalizing a recent such principle for C*-algebras
exhibited in work of Castillejos et al. For actions on simple nuclear
$\mathcal{Z}$-stable C*-algebras, we use this to prove that equivariant uniform
property Gamma is equivalent to equivariant $\mathcal{Z}$-stability,
generalizing a result of Gardella-Hirshberg-Vaccaro.
