  We compute the next-to-leading order (NLO) hard correction to the gluon
self-energy tensor with arbitrary soft momenta in a hot and/or dense weakly
coupled plasma in Quantum Chromodynamics. Our diagrammatic computations of the
two-loop and power corrections are performed within the hard-thermal-loop (HTL)
framework and in general covariant gauge, using the real-time formalism. We
find that after renormalization our individual results are finite and
gauge-dependent, and they reproduce previously computed results in Quantum
Electrodynamics in the appropriate limit. Combining our results, we also
recover a formerly known gauge-independent matching coefficient and associated
screening mass in a specific kinematic limit. Our NLO results supersede
leading-order HTL results from the 1980s and pave the way to an improved
understanding of the bulk properties of deconfined matter, such as the equation
of state.
