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We address the long-standing problem of the structure of the low-energy eigenstates and long-time coherent dynamics in quantum spin-glass models. Below the spin-glass freezing transition, the energy landscape of the spin system is characterized by a proliferation of local minima where classical dynamics gets trapped. A theoretical description of quantum dynamics in this regime is challenging due to the complex nature of the distribution of the tunneling matrix elements between the local minima of the energy landscape. We study the transverse-field-induced quantum dynamics of the following “impurity band”(IB) spin model: zero energy of all spin configurations except for a small fraction of spin configurations (“marked states”) that form a narrow band at a large negative energy. At a zero transverse field, the IB model demonstrates the freezing transition at inverse temperature β f∼ 1 characterized by a nonzero …