Motivated by automotive applications, we consider joint radar sensing and data communication for a system operating at millimeter wave (mmWave) frequency bands, where a Base Station (BS) is equipped with a co-located radar receiver and sends data using the Orthogonal Time Frequency Space (OTFS) modulation format. We consider two distinct modes of operation. In Discovery mode, a single common data stream is broadcast over a wide angular sector. The radar receiver must detect the presence of not yet acquired targets and perform coarse estimation of their parameters (angle of arrival, range, and velocity). In Tracking mode, the BS transmits multiple individual data streams to already acquired users via beamforming, while the radar receiver performs accurate estimation of the aforementioned parameters. Due to hardware complexity and power consumption constraints, we consider a hybrid digital-analog architecture where the number of RF chains and A/D converters is significantly smaller than the number of antenna array elements. In this case, a direct application of the conventional MIMO radar approach is not possible. Consequently, we advocate a beam-space approach where the vector observation at the radar receiver is obtained through a RF-domain beamforming matrix operating the dimensionality reduction from antennas to RF chains. Under this setup, we propose a likelihood function-based scheme to perform joint target detection and parameter estimation in Discovery, and high-resolution parameter estimation in Tracking mode, respectively. Our numerical results demonstrate that the proposed approach is able to reliably detect multiple targets while closely approaching the Cramer-Rao Lower Bound (CRLB) of the corresponding parameter estimation problem.