How can I run shortcode after click with ajax
You should try to replace the following jQuery part: action: ‘process_shortcode_on_tab_click’ with this one: action: ‘process_shortcode_on_tab_click_action’ to match your wp_ajax_process_shortcode_on_tab_click_action and wp_ajax_nopriv_process_shortcode_on_tab_click_action actions. Check for example the Codex on how to name the custom wp_ajax_$youraction hook.