How to show only next post pagination link using wp_link_pages()

Here’s a suggestion, using the wp_link_pages_link filter to remove the previous links:

add_filter( 'wp_link_pages_link', function( $link, $nextorprev )
{   
    return get_query_var( 'page' ) > $nextorprev ? '' : $link;

}, 10, 2 );

We can also create a plugin that removes empty previous/next links.

So if we have one of the following:

'nextpagelink' => '',
'nextpagelink' => false,
'nextpagelink' => null,

'previouspagelink' => '',
'previouspagelink' => false,
'previouspagelink' => null,

then these links will be removed.

Here’s the skeleton for such a plugin:

<?php
/** 
 * Plugin Name: Remove Empty Next/Previous Content Pagination Links 
 * Plugin URI:  http://wordpress.stackexchange.com/a/239335/26350
 */

add_filter( 'wp_link_pages_args', function( $args )
{
    if( empty( $args['previouspagelink'] ) )
        add_filter( 'wp_link_pages_link', 'wpse_remove_prev_links', 10, 2 );

    if( empty( $args['nextpagelink'] ) )
        add_filter( 'wp_link_pages_link', 'wpse_remove_next_links', 10, 2 );

    return $args;       
} );

add_filter( 'wp_link_pages', function( $output, $args )
{
    if( empty( $args['previouspagelink'] ) )
        remove_filter( 'wp_link_pages_link', 'wpse_remove_prev_links', 10, 2 );

    if( empty( $args['nextpagelink'] ) )
        remove_filter( 'wp_link_pages_link', 'wpse_remove_next_links', 10, 2 );     

    return $output;
}, 10, 2 );

function wpse_remove_prev_links( $link, $nextorprev )
{
    return get_query_var( 'page' ) > $nextorprev ? '' : $link;
}

function wpse_remove_next_links( $link, $nextorprev )
{
    return get_query_var( 'page' ) < $nextorprev ? '' : $link;
}

This will not override the default settings, if we leave out the ‘nextpagelink’ or ‘previouspagelink’ arguments.

Here’s a way to add a custom link at the last page:

add_filter( 'wp_link_pages_link', function( $link, $nextorprev ) use ( &$numpages )
{   
    return get_query_var( 'page' ) === $numpages ? 'CUSTOM LINK' : $link;

}, 11, 2 );

where we have the priority later than in our plugin.

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