Networks of autonomous underwater hydrophones (AUHs) are successfully employed for monitoring the low‐level seismicity of mid‐oceanic ridges by detecting hydroacoustic phases known as T waves. For a precise localization of a seismic event from T‐wave arrival times, all AUHs must be synchronized. To this effect, at the beginning of the experiment, all instrument clocks are set to GPS time, which serves as a common reference. However, during the experiment, the instrument clock often deviates from GPS time, and, because the amount of deviation differs from one instrument to another, the synchronization of the AUHs deteriorates, as the experiment progresses in time. Just after the instrument recovery, the time difference (called “skew”) between the instrument and the GPS clocks is measured. Assuming that the skew varies linearly with time, the correction of a time series for the clock drift is a straightforward procedure. When the final skew cannot be determined, correcting for the clock drift is not possible, and any event localization becomes problematic. In this article, we demonstrate that the clock‐drift rate (assumed to be time‐independent) can be successfully estimated from arrival times of teleseismic P waves, commonly recorded by AUHs. Using a ray‐tracing code, and accounting for the uncertainties in event hypocenter locations, origin times, and the Earth seismic‐velocity model, confidence intervals of the estimated drift rates are deduced. The validity of the approach is tested on data from two AUHs with known clock drifts. Our results show that a reliable estimation is possible for skews as small as 4 s per two years (corresponding to a drift rate of about 5.5  ms⋅day−1⁠). This method can also be applied to correct data of other recording instruments subject to internal‐clock drift, such as ocean‐bottom seismometers, when the skew is unknown.