You can use beforeSend ajax event
It could be something like this (code not tested)
jQuery.post(the_ajax_script.ajaxurl, jQuery(".form_branch").serialize(),function(response_from_display_data_table){
jQuery(".table_disp").html(response_from_display_data_table);
}).beforeSend(display_table_1());
or, the other way around:
jQuery.post(the_ajax_script.ajaxurl, jQuery(".form_year").serialize(),function(response_from_display_data_table_1){
jQuery(".table_disp").html(response_from_display_data_table_1);
}).beforeSend(display_table());