  We investigate whether supertranslation symmetry may appear in a scenario
that involves black holes in AdS space. The framework we consider is massive 3D
gravity, which admits a rich black hole phase space, including stationary AdS
black holes with softly decaying hair. We consider a set of asymptotic
conditions that permits such decaying near the boundary, and which, in addition
to the local conformal symmetry, is preserved by an extra local current. The
corresponding algebra of diffeomorphisms consists of two copies of Virasoro
algebra in semi-direct sum with an infinite-dimensional Abelian ideal. We then
reorient the analysis to the near horizon region, where infinite-dimensional
symmetries also appear. The supertranslation symmetry at the horizon yields an
infinite set of non-trivial charges, which we explicitly compute. The zero-mode
of these charges correctly reproduces the black hole entropy. In contrast to
Einstein gravity, in the higher-derivative theory subleading terms in the near
horizon expansion contribute to the near horizon charges. Such terms happen to
capture the higher-curvature corrections to the Bekenstein area law.
