The presence of an obscuring torus at parsec-scale distances from the central black hole is the main ingredient for the Unified Model of Active Galactic Nuclei (AGN), as obscured sources are thought to be seen through this structure. However, the Unified Model fails to describe a class of sources that undergo dramatic spectral changes, transitioning from obscured to unobscured and vice-versa through time. The variability in such sources, so-called Changing Look AGN (CLAGN), is thought to be produced by a clumpy medium at much smaller distances than the conventional obscuring torus. ESO 323-G77 is a CLAGN that was observed in various states through the years with Chandra, Suzaku, Swift-XRT and XMM-Newton, from unobscured (N H < 3×10 22 cm −2 ) to Compton-thin (N H ∼ 1 − 6 × 10 23 cm −2 ) and even Compton-thick (N H > 1 × 10 24 cm −2 ), with timescales as short as one month. We present the analysis of the first NuSTAR monitoring of ESO 323-G77, consisting of 5 observations taken at different timescales (1, 2, 4 and 8 weeks from the first one) in 2016-2017, in which the AGN was caught in a persistent Compton-thin obscured state (N H ∼ 2 − 4 × 10 23 cm −2 ). We find that a Compton-thick reflector is present (N H,refl = 5 × 10 24 cm −2 ), most likely associated with the presence of the putative torus. Two ionized absorbers are unequivocally present, located within maximum radii of r max,1 = 1.5 pc and r max,2 = 0.01 pc. In one of the observations, the inner ionized absorber is blueshifted, indicating the presence of a possible faster (v out = 0.2c) ionized absorber, marginally detected at 3σ. Finally, we are able to constrain the coronal temperature and the optical depth of ESO 323-G77, obtaining kT e = 38 keV or kT e = 36 keV, and τ = 1.4 or τ = 2.8, depending on the coronal geometry assumed.