This paper presents a BeppoSAX observation of NGC 7582 made during 1998 November and an optical spectrum taken in 1998 October. The new X-ray data reveal a previously unknown hard X-ray component in NGC 7582, peaking close to 20 keV. Rapid variability is observed with correlated changes in the 5-10 and 13-60 keV bands indicating that a single continuum component, produced by the active nucleus, provides the dominant flux across both bands. Changes in the nuclear X-ray flux appear unrelated to the gradual decline in optical flux noted since the high-state in 1998 July. The X-ray continuum is attenuated by a thick absorber of N_H ~ 1.6 x 10E24 cm^-2 covering ~60% of the nucleus, plus a screen with N_H ~ 1.4 x 10E23 cm^-2 covering the entire nucleus. Comparison of the BeppoSAX and ASCA spectra shows an increase in the full screen by N_H ~7 x 10E22 cm^-2 since 1994, confirming the absorption variability found by Xue et al. The increase in soft X-ray flux between 1994 and 1998 is consistent with the appearance of holes in the full screen producing some clear lines-of-sight to the broad-line-region.
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