Are there examples of closed hyperbolic $n$-manifolds $M$ that have the first Betti number equal to one, $b_1(M) = 1$, such that $n \geq 4$?
I am aware that there are such examples for $n = 3$, using the Thurston-Nielsen classification and the abundance of pseudo-Anosov maps on surfaces with prescribed action on $H^1$. According to B. Martelli (see below) there is an example with $n = 4$ and $b_1(M) = 2$, called the ``Conder–Maclachlan manifold".
Martelli, Bruno, Hyperbolic four-manifolds, ZBL07034448.