This letter proposes a new control scheme for the provision of adaptive inertial response by virtual synchronous generators. In contrast to state-of-the-art methods, the proposed strategy proactively allocates higher inertia values at the onset of frequency disturbances while respecting the energy limits of the associated energy storage system. The performance of the developed technique is assessed by means of rms simulations on the IEEE 39-bus system. The results demonstrate that the proposed scheme enhances the dynamic performance of the power system by reducing the rate of change of frequency and delaying the occurrence of the frequency extrema (nadir/zenith).