In this paper, we study peak age of information (PAoI) performance of a novel IoT solution for remote health-monitoring of first responders over TErrestrial Trunked RAdio (TETRA) links. The solution features a set of sensors embedded in a smart garment that periodically record and send physiological parameters of first responders to a remote agent. The received data is analyzed by the remote agent, which feeds back notifications and warnings to the first responders in the form of electrotactile stimuli. The communication in the system is performed over the TETRA Short Data Service (SDS), which is the default option for the development of third-party applications and which has rather limited capabilities. The choice of the PAoI as the parameter of interest is motivated by its suitable to measure data freshness in IoT applications with periodic monitoring. We derive closed-form expressions of PAoI for different packet-management schemes allowed by the TETRA standard, and verify the analytical results through extensive simulations under varying message generation rates. Our results provide important insights on the expected PAoI performance, which can be used for the system design guidelines. To the best of our knowledge, this is the first work that analyzes AoI performance of TETRA networks.