The first thing you’re going to need to add is field groups to the form call itself to even get the form to display, then you need to add specifics to tell ACF where to put the new post.
<?php
$args = array(
'field_groups' => array('group_678906ab8ec')),
'post_id' => 'new_post',
'new_post' => array(
'post_type' => 'application ',
'post_status' => 'pending'
),
'submit_value' => 'Submit Application'
);
acf_form();
?>