The GRACE satellites have been operating in space for more than 15 years. Over this period, not only unique time series of monthly models were accumulated, but also the methods for data processing and suppression of different errors, primarily related to different sensitivity along and across the orbit, were substantially improved. This allowed the number of spherical harmonics in the GRACE monthly models to be increased from 40 up to 80 and even 96. This, in particular, opened new opportunities for investigating postseismic processes in the regions of major earthquakes. In this paper we discuss possible geodynamic processes that may be responsible for the growth of a positive gravity-field anomaly after the Simushir earthquake on November 15, 2006. The growth started a few months after this event and coincided in time with the activation of seismicity on the continuation of the zone of the coseismic rupture in depth. Numerical simulation using data from GPS stations and temporal variations of the gravity field has shown that the viscoelastic relaxation of stresses resulting from an earthquake plays a subordinate role. The main process that is responsible for postseismic displacements and the growth of the gravity anomaly is the postseismic creep in a vast zone around the coseismic rupture, including its continuation to a depth of 100 km.