We explore the impact on the outer radiation belt of significant time-integrated ap events of continuously elevated geomagnetic activity, making use of Van Allen Probes measurements in 2013-2017. We show that most high peaks of 1.8-MeV electron flux occur during the 10 days immediately following such events, with stronger events leading to higher flux. Events larger than 800 nT•hr are always followed by a high peak of flux in the heart of the outer radiation belt. They lead to 10-day-averaged 1.8-MeV electron fluxes of the order of 10 6 e/cm 2 /sr/s/MeV in this region and 8 × 10 4 e/cm 2 /sr/s/MeV near geostationary orbit. Accordingly, they can be considered as reliable precursors of high peaks of 2-MeV electron flux throughout the outer belt. We demonstrate that the flux peaks following such significant events can be parameterized by different geomagnetic indices at different radial locations in 2013-2017. Comparisons between the corresponding modeled flux peaks and observations show a reasonable agreement for both the timing, duration, and level of the peaks with 2015 data from the Van Allen Probes and also with 2002-2012 data from Global Positioning System satellites and 2003-2016 data from Geostationary Operational Environmental Satellites, provided that dropouts are taken into account via an appropriate threshold on solar wind dynamic pressure. Plain Language Summary Considering significant events of prolonged and elevated geomagnetic activity measured at middle-latitude stations, we examine their effects on megaelectron volt electron fluxes that represent an important hazard for satellites throughout the outer radiation belt. Using measurements performed by the Van Allen Probes in 2013-2017, we find that high peaks of 1.8-MeV electron flux appear in the immediate aftermath of all events in the heart of the outer radiation belt and last about 10 days. Such events can therefore be considered as reliable precursors of high flux peaks. The statistical dependence of flux peaks on different measures of precursor event strength and radial distance is obtained. The reliability of such a description over the long term is tested by comparisons with earlier measurements from other satellites in 2002-2012, further taking dropouts into account. These results should be useful for better understanding the effects of geomagnetic disturbances on megaelectron volt electrons and to improve forecasts of the timing and level of such peaks of 2-MeV electron flux.