  Fix a positive integer $g$ and rational prime $p$. We prove the existence of
a genus $g$ curve $C/\mathbb{Q}$ such that the mod $p$ representation of its
Jacobian is tame by imposing conditions on the endomorphism ring. As an
application, we consider the tame inverse Galois problem and are able to
realise general symplectic groups as Galois groups of tame extensions of
$\mathbb{Q}$.
