The Italian National Institute for Astrophysics (INAF) is leading the ASTRI Project, whose main objective in the early years was the design, development and deployment of an end-to-end dual- mirror 4-m diameter prototype of the Cherenkov Telescope Array Observatory (CTAO) small-sized telescopes (SSTs) for gamma-ray astronomy in the 1–200 TeV energy range. The prototype, named the ASTRI-Horn telescope, is located on Mount Etna (Italy) and features innovative solutions, such as a dual-mirror aplanatic optical system and a Cherenkov camera based on silicon photo-multiplier (SiPM) detectors. After achieving in the past years the first optical validation (2017) and the first detection at TeV energies of a gamma-ray source (2018) by a Cherenkov telescope in dual-mirror Schwarzschild-Couder configuration, in recent years (2020-2022) the ASTRI-Horn telescope underwent significant maintenance and refurbishment to restore damaged systems and improve technical performance. The telescope is currently fully operational and carries on different scientific programs, including gamma-ray, cosmic-ray, and muon-radiography of the Etna volcano investigations. In particular, in the period between fall 2022 and spring 2023, a new observing campaign on the Crab Nebula source was carried out to evaluate the new telescope performance. In this contribution, we present the Crab Nebula data sample collected by the ASTRI-Horn telescope in the aforementioned campaign and discuss some preliminary results.