  In this paper, we investigate the Tomas-Stein restriction estimates on convex
cocompact hyperbolic manifolds $\Gamma\backslash\mathbb{H}^{n+1}$. Via the
spectral measure of the Laplacian, we prove that the Tomas-Stein restriction
estimate holds when the limit set has Hausdorff dimension $\delta_\Gamma<n/2$.
This provides an example for which restriction estimate holds in the presence
of hyperbolic geodesic trapping.
