By measuring the nuclear magnetic resonance (NMR) T −1 1 relaxation rate in the Br (bond) doped DTN compound, Ni(Cl1−xBrx)2-4SC(NH2)2 (DTNX), we show that the low-energy spin dynamics of its high magnetic field "Bose-glass" regime is dominated by a strong peak of spin fluctuations found at the nearly doping-independent position H * ∼ = 13.6 T. From its temperature and field dependence we conclude that this corresponds to a level crossing of the energy levels related to the doping-induced impurity states. Observation of the local NMR signal from the spin adjacent to the doped Br allowed us to fully characterize this impurity state. We have thus quantified a microscopic theoretical model that paves the way to better understanding of the Bose-glass physics in DTNX, as revealed in the related theoretical study [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017) The NiCl 2 -4SC(NH 2 ) 2 (DTN) compound [1], consisting of weakly coupled chains of S = 1 (Ni-ion) spins with an easy-plane single-ion anisotropy (D), is one of the most studied quantum spin materials [2]. Between the two critical magnetic fields H c1 and H c2 , it presents a magnetic-field-induced low-temperature (T ) 3D-ordered phase, described as a Bose-Einstein condensate (BEC) [2][3][4][5]. DTN is particularly convenient for studying this phase; for a magnetic field (H) applied along the chain c axis, its (body-centered) tetragonal symmetry [6] ensures the required axial symmetry of the spin Hamiltonian with respect to H. The values of its exchange couplings and [7,8] make the BEC phase easily accessible, with H c2 = 12.32 T [9-11] and the phase transition temperature T c below T cmax = 1.2 K. The system can be reasonably considered as quasi-one-dimensional (1D), with J a,b /J c = 0.08.Br-doped DTN, Ni(Cl 1−x Br x ) 2 -4SC(NH 2 ) 2 (DTNX), allows studying the effect of a bond disorder, which may lead to the appearance of a localized Bose-glass (BG) phases adjacent to the (now inhomogeneous) BEC phase [12], as suggested from the thermodynamic measurements [13]. The BG state, first discussed for quantum wires [14] and superfluid 4 He absorbed in porous media [15,16], remains elusive, with only a few experimental examples [17][18][19][20], particularly rare for condensed-matter systems in the thermodynamic limit [21], such as DTNX [13].We present here the first microscopic information on the high-field (H > H c2 ) disordered state in DTNX, where the low-energy spin fluctuations (dynamics) are measured by 1 H and 14 N nuclear spin-lattice relaxation rate (T −1 1 ), while the NMR spectra revealed the local spin polarization [22]. As compared to pure DTN, the main feature of spin dynamics in DTNX is a peak of T −1 1 appearing at H * ∼ = 13.6 T independently of the doping level. This is attributed to the level crossing of singleparticle states strongly localized at the doped-bond position, which is then somewhat distributed/disordered by the mutual interaction of these states. The disorder is seen by NMR as the inhomogeneous relaxat...