You can add following code in your theme’s (child theme’s if any) functions.php

add_filter( 'fep_directory_output', function( $output ){
	$pos = strpos( $output, '<input type="hidden" name="feppage"' );
	if ( $pos !== false ) {
		$output = substr_replace( $output, '<input type="submit" value="Search" />', $pos, 0 );
	}
	return $output;
});

it may break in future.

OR you can override directory.php template to add that button. Instruction to override template in https://www.shamimsplugins.com/docs/front-end-pm-pro/customization-front-end-pm-pro/change-templates/