Mechanisms of rearrangement process in a defect-bearing solid hydrogen-bonded network system -a clathrate hydrate encaging polar guest-are examined in terms of the waiting time distribution functions for connectivity changes of water molecules. As previously found for the lifetime distributions of hydrogen bonds in supercooled water by Sciortino et al., a power-law-like behavior is observed for the waiting time distribution in short-time region in the clathrate hydrates; in long time region the distribution is close to an exponential form. It is revealed that the behavior is accounted for by assuming two kinds of processes of the connectivity changes : one is caused by thermal excitation in a perfect network region, which can be regarded as a Poisson process and another is induced by defects in the environmental network, which is responsible for the power-law-like behavior. Also the waiting time for the defect-induced connectivity changes of a molecule is related to how many other molecules are involved in local network rearrangement processes. By a simple model of single-axis rotator for reorientational jumps of a water molecule, we show that a power-law-like behavior appears in the dipole autocorrelation function when the waiting time for jump events is a strong power-law type distribution as observed in the defect-induced connectivity changes.