In this exploratory work, we have examined the impact of an external static electric field on the H2 storage capacity of clathrate hydrates. To this end, we have chosen the 512 clathrate hydrate and examined the encapsulation of 1 - 4 H2 molecules within it. Results suggest that with the help of moderate electric fields (±0.10 to ±0.31V/Å), the encapsulation of 1 H2 molecule within the 512 clathrate hydrate becomes thermodynamically more favorable. In the cases of 4H2@512 and 2H2@512, however, the concerned processes become thermodynamically more favorable only when the field is applied along a specific direction. No favorable outcome could be observed in the case of 3H2@512, irrespective of the direction of the applied field. It appears from the results obtained herein that it might be possible to design a suitable external electric field to facilitate the hydrogen storage capacity of clathrate hydrates at ambient conditions, at least in certain cases.