An excited metastable nuclear state of Os-192 in a hydrogen-like charge state has been studied for the first time. It was populated in projectile fragmentation of a Au-197 beam on a Be-9 target with the UNILAC-SIS accelerators at GSI. Fragmentation products in the region of interest were passed through the fragment separator and injected into the experimental storage ring (ESR). Cooling of the injected beam particles enabled Schottky mass spectrometry to be performed. Analysis shows the lifetime of the state to be considerably longer than that of the neutral ion [tau(neut) = 8.5(14) s]; this change is attributed to hindrance of internal conversion in hydrogen-like Os-192. Calculations have been performed to estimate the lifetime, and the result has been compared with that measured experimentally. There is good agreement between the expected [tau(H-like) = 13.0(24) s] and measured lifetimes (tau(rest) = 15.1(-1.3)(+1.5) s) from the internal decay of Os-192m. This provides a test for the reliability of the values obtained from internal conversion coefficient calculations in highly ionized systems and is the first measurement of its kind to be performed using the ESR setup.