We suggest a novel paradigm to achieve strong nonreciprocal plasmonic responses and optical gain based on the biasing of a graphene sheet with a drift electric current. In particular, we theoretically demonstrate that a drift-current biasing of a graphene sheet leads to the emergence of unidirectional and backscattering-immune plasmons with enhanced propagation length. We show that the drift-current biasing may give rise to gain regimes wherein the graphene plasmons acquire energy from the drifting electrons. Moreover, we demonstrate that by taking advantage of the gain effect, it is possible to obtain regimes of loss compensation or even of plasmon amplification in systems formed by a drift-current biased graphene sheet coupled to a plasmonic slab.