Early results from the JWST observations have reported a surprisingly high number of UV-bright galaxies at z ≥ 10, which appears to challenge the theoretical predictions from standard galaxy formation models in the ΛCDM framework at these redshifts. To alleviate this tension, several cosmological and astrophysical interpretations have been advanced. However, all of these proposed scenarios carry noteworthy consequences for other large-scale processes in the early Universe, particularly cosmic reionization, since high-redshift galaxies are believed to be the primary ionizing sources during the Epoch of Reionization (EoR). To investigate this, we introduce a semi-analytical model of galaxy formation and evolution that explains the evolving galaxy UV luminosity function (UVLF) over 6 ≲ z ≲ 15, and also jointly tracks the time evolution of the globally averaged neutral hydrogen fraction in the intergalactic medium. The model self-consistently accounts for the suppression of star formation in low-mass galaxies due to reionization feedback and is constrained by comparing the model predictions with various observational probes like the UVLF data from HST and JWST, recent measurements of the neutral hydrogen fraction, and the CMB scattering optical depth. Our analysis confirms that a rapid enhancement in the star-formation rate efficiency and/or UV luminosity per stellar mass formed is necessary for consistency with the JWST UVLF estimates at z ≥ 10. We further find that it is possible to jointly satisfy the current reionization constraints when the escape fraction is assumed to be halo-mass dependent, requiring higher Lyman-continuum leakage from low-mass galaxies. We also examine the relative contribution of galaxies with different UV luminosities towards the ionizing photon budget for the EoR and investigate the large-scale bias of high-z galaxies.