A fibration of a manifold $\phi: M \to S^1$ gives rise to a short exact sequence $$ 1 \to \pi_1(N) \to \pi_1(M) = \mathbb{Z} \overset{f_\ast}{\to} 1 $$ where $N$ is the fiber.

I've heard that, if $M$ is a hyperbolic 3-manifold, $\pi_1(N)$ is finitely generated or even finitely presented. Is that true and if so, why?