  Let $\Gamma$ be a Zariski dense convex cocompact subgroup contained in an
arithmetic lattice of $\operatorname{SO}(n, 1)^{\circ}$. We prove uniform
exponential mixing of the geodesic flow for congruence covers of the hyperbolic
manifold $\Gamma \backslash \mathbb{H}^n$ avoiding finitely many prime ideals.
This extends the work of Oh-Winter who proved the result for the $n = 2$ case.
Following their approach, we use Dolgopyat's method for the proof of
exponential mixing of the geodesic flow. We do this uniformly over congruence
covers by establishing uniform spectral bounds for the congruence transfer
operators associated to the geodesic flow. This requires another key ingredient
which is the expander machinery due to Bourgain-Gamburd-Sarnak extended by
Golsefidy-Varj\'{u}.
