We present a hard X-ray observation of the TeV gamma-ray binary candidate HESS J1832 - 093 coincident with supernova remnant ( SNR ) G22.7 - 0.2 using the Nuclear Spectroscopic Telescope Array ( NuSTAR ) . Non-thermal X-ray emission from XMMU J183245 - 0921539 , the X-ray source associated with HESS J1832 - 093 , is detected up to \sim 30 keV and is well-described by an absorbed power-law model with the best-fit photon index \Gamma = 1.5 \pm 0.1 . A re-analysis of archival Chandra and XMM-Newton data finds that the long-term X-ray flux increase of XMMU J183245 - 0921539 is 50 _ { -20 } ^ { +40 } % ( 90 % C.L . ) , much less than previously reported . A search for a pulsar spin period or binary orbit modulation yields no significant signal to a pulse fraction limit of f _ { p } < 19 % in the range 4 ms < P < 40 ks . No red noise is detected in the FFT power spectrum to suggest active accretion from a binary system . While further evidence is required , we argue that the X-ray and gamma-ray properties of XMMU J183245 - 0921539 are most consistent with a non-accreting binary generating synchrotron X-rays from particle acceleration in the shock formed as a result of the pulsar and stellar wind collision . We also report on three nearby hard X-ray sources , one of which may be associated with diffuse emission from a fast-moving supernova fragment interacting with a dense molecular cloud .