This paper investigates the joint impact of nodes' mobility and imperfect channel estimates on the secrecy performance of an underlay cognitive radio vehicular network over Nakagami-m fading channels. Specifically, the secondary network consists of a single-antenna source vehicle, an N _D -antenna destination vehicle, and an N _E -antenna passive eavesdropper vehicle, whereas the primary network comprises of a single-antenna primary receiver vehicle. The time selective fading links arise due to nodes' mobility are modeled via first-order auto-regressive process, and the channel state information is estimated using linear minimum mean square error estimation method. Moreover, the transmit power of secondary source is constrained by both the interference threshold of the primary receiver and the maximum transmit power of secondary network. Under such a realistic scenario, we derive the analytical closed-form secrecy outage probability (SOP) and ergodic secrecy capacity expressions. Furthermore, we present asymptotic SOP analysis to obtain key insights into the system's secrecy diversity order. We also report several practical cases of interest to reveal valuable information about the system's secrecy behavior. Moreover, we illustrate the impacts of system/channel parameters, nodes' mobility, imperfect channel estimates, interference temperature limit, and the maximum available source power. Finally, the simulation studies corroborate our derived analytical findings.