Although ZwCl0024+1652 galaxy cluster at z ∼ 0.4 has been thoroughly analysed, it lacks a comprehensive study of star formation and nuclear activity of its members. With GaLAxy Cluster Evolution (GLACE) survey, a total of 174 H α emission-line galaxies (ELGs) were detected, most of them having [N II]. We reduced and analysed a set of [O III] and H β tunable filter (TF) observations within GLACE survey. Using H α priors, we identified [O III] and H β in 35 (∼20 per cent) and 59 (∼34 per cent) sources, respectively, with 21 of them having both emission lines, and 20 having in addition [N II]. Applying BPT-NII diagnostic diagram, we classified these ELGs into 40 per cent star-forming (SF), 55 per cent composites, and 5 per cent LINERs. Star formation rate (SFR) measured through extinction corrected H α fluxes increases with stellar mass (M*), attaining its peak at $\mathrm{\mathit{ M}}_{*}\sim 10^{9.8}\, \mathrm{M}_\odot$ . We observed that the cluster centre to ∼ 1.3 Mpc is devoid of SF galaxies and AGN. Our results suggest that the star formation efficiency declines as the local density increases in the cluster medium. Moreover, the SF and AGN fractions drop sharply towards high-density environments. We observed a strong decline in SF fraction in high M*, confirming that star formation is highly suppressed in high-mass cluster galaxies. Finally, we determined that SFR correlates with M* while specific SFR (sSFR) anticorrelates with M*, both for cluster and field. This work shows the importance and strength of TF observations when studying ELGs in clusters at higher redshifts. We provide with this paper a catalogue of ELGs with H β and/or [O III] lines in ZwCl0024+1652 cluster.