Ok, this might be overcomplicating things a bit, but at least it should work (untested).
Just call the function like so
get_adjacent_without_sticky( get_the_ID(), true); // get previous post
get_adjacent_without_sticky( get_the_ID(), false); // get next post
This could have been solved easily, if get_previous_post() allowed for an ID to pass and not only run it in the context of the current post. Now you could copy the function code of get_adjacent_post() and adjust it to your needs, but I don’t like messing directly with SQL inside WordPress, so using the common functions it should work like this:
function get_adjacent_without_sticky($id, $previous = true) {
// get date of current post as reference
$date = explode('.', get_the_date('d.m.Y', $id));
$date_array = array(
'day' => $date[0],
'month' => $date[1],
'year' => $date[2],
);
// for previous post we need the first post before current one
if ($previous) {
$order="DESC";
$date_query = array(
'before' => $date_array,
);
}
// for next post we need the first post after current one
else {
$order="ASC";
$date_query = array(
'after' => $date_array,
);
}
$args = array(
// order sticky posts as regular ones
'ignore_sticky_posts' => 1,
// get only the one post we want
'posts_per_page' => 1,
'order' => $order,
'orderby' => 'date',
'date_query' => $date_query,
);
// now run that query
$the_query = new WP_Query($args);
if ($the_query->have_posts()) {
$the_query->the_post();
$result = get_post( get_the_ID() );
} else {
$result = NULL;
}
wp_reset_postdata(); // Restore original Post Data
return $result;
}
Related topics:
(My answer is bascially these two sources combined into a function.)