The theory of superconductivity developed by Bardeen, Cooper and Schrieffer (BCS) explains the stabilization of electron pairs into a spin-singlet, even frequency, state by the formation of an energy gap within which the density of states is zero. At a superconductor interface with an inhomogeneous ferromagnet, a gapless odd frequency superconducting state is predicted, in which the Cooper pairs are in a spin-triplet state. Although indirect evidence for such a state has been obtained, the gap structure and pairing symmetry have not so far been determined. Here we report scanning tunnelling spectroscopy of Nb superconducting films proximity coupled to epitaxial Ho. These measurements reveal pronounced changes to the Nb subgap superconducting density of states on driving the Ho through a metamagnetic transition from a helical antiferromagnetic to a homogeneous ferromagnetic state for which a BCS-like gap is recovered. The results prove odd frequency spin-triplet superconductivity at superconductor/inhomogeneous magnet interfaces.