The invention relates to a hydraulic tappet clearance compensation device (1) for a valve gear of an internal combustion engine, the high pressure chamber (8) of which device can be rapidly and easily vented. For this purpose an annular collar (11) has radial openings (16) distributed over the circumference of its pressure piston (5). These allow air bubbles, which accumulate between an outer shell of the annular collar (11) and a bore (3) of a housing (2), to escape to a bore (9) for a non-return valve (10) and hence directly into the open. There is therefore no need for venting via a leakage gap (13) between the pressure piston (5) and the housing (2), which has hitherto yielded only unsatisfactory results.