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Abstract Theoretical models predict thatz≳ 6 quasars are hosted in the most massive halos of the underlying dark matter distribution and thus would be immersed in protoclusters of galaxies. However, observations report inconclusive results. We investigate the 1.1 proper-Mpc²environment of thez= 7.54 luminous quasar ULAS J1342+0928. We search for Lyman-break galaxy (LBG) candidates using deep imaging from the Hubble Space Telescope (HST) in the Advanced Camera for Surveys (ACS)/F814W, Wide Field Camera 3 (WFC3)/F105W/F125W bands, and Spitzer/Infrared Array Camera at 3.6 and 4.5μm. We report a $z_{\mathrm{phot}}={7.69}_{-0.23}^{+0.33}$LBG with mag_F125W= 26.41 at 223 projected proper kpc (pkpc) from the quasar. We find no HST counterpart to one [Cii] emitter previously found with the Atacama Large millimeter/submillimeter Array (ALMA) at 27 projected pkpc andz_{[C II]}=7.5341 ± 0.0009 (Venemans et al. 2020). We estimate the completeness of our LBG candidates using results from Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey/GOODS deep blank field searches sharing a similar filter setup. We find that >50% of thez∼ 7.5 Lyman-break galaxies (LBGs) with mag_F125W> 25.5 are missed due to the absence of a filter redward of the Lyman break in F105W, hindering the UV color accuracy of the candidates. We conduct a QSO-LBG clustering analysis revealing a low LBG excess of ${0.46}_{-0.08}^{+1.52}$in this quasar field, consistent with an average or low-density field. Consequently, this result does not present strong evidence of an LBG overdensity around ULAS J1342+0928. Furthermore, we identify two LBG candidates with az_photmatching a confirmedz= 6.84 absorber along the line of sight to the quasar. All these galaxy candidates are excellent targets for follow-up observations with JWST and/or ALMA to confirm their redshift and physical properties.