Custom fields are not stored as part of the standard WP term information and they cannot be accessed like this. This is similar to to custom fields on posts.
For posts you need to use get_post_meta() to get the field in WP. With ACF you use get_field(). For term custom fields you still use the same ACF function but you must supply a post ID. You wan to echo the value so you can use the_field()
<?php
$post_id = $member_group_term->taxonomy.’_’.$member_group_term->term_id;
the_field(‘mep_party_link’, $post_id);
?>
