For 15 years, the Gravity Recovery and Climate Experiment (GRACE) mission have monitored total water storage (TWS) changes. The GRACE mission ended in October 2017, and 11 months later, the GRACE Follow-On (GRACE-FO) mission was launched in May 2018. Bridging the gap between both missions is essential to obtain continuous mass changes. To fill the gap, we propose a new approach based on a remove–restore technique combined with an autoregressive (AR) prediction. We first make use of the Global Land Data Assimilation System (GLDAS) hydrological model to remove climatology from GRACE/GRACE-FO data. Since the GLDAS mis-models real TWS changes for many regions around the world, we further use least-squares estimation (LSE) to remove remaining residual trends and annual and semi-annual oscillations. The missing 11 months of TWS values are then predicted forward and backward with an AR model. For the forward approach, we use the GRACE TWS values before the gap; for the backward approach, we use the GRACE-FO TWS values after the gap. The efficiency of forward–backward AR prediction is examined for the artificial gap of 11 months that we create in the GRACE TWS changes for the July 2008 to May 2009 period. We obtain average differences between predicted and observed GRACE values of at maximum 5 cm for 80% of areas, with the extreme values observed for the Amazon, Alaska, and South and Northern Asia. We demonstrate that forward–backward AR prediction is better than the standalone GLDAS hydrological model for more than 75% of continental areas. For the natural gap (July 2017–May 2018), the misclosures in backward–forward prediction estimated between forward- and backward-predicted values are equal to 10 cm. This represents an amount of 10–20% of the total TWS signal for 60% of areas. The regional analysis shows that the presented method is able to capture the occurrence of droughts or floods, but does not reflect their magnitudes. Results indicate that the presented remove–restore technique combined with AR prediction can be utilized to reliably predict TWS changes for regional analysis, but the removed climatology must be properly matched to the selected region.