Link for Most Recent Post

You’ll need to use get_posts() to get the latest post, then pass it to get_the_permalink() to get the URL to it:

<?php 
$latest_posts = get_posts( array( 'numberposts' => 1 ) );

if ( ! empty( $latest_posts ) ) :
    $latest_post = $latest_posts[0];

    if ( $latest_post->ID !== get_the_ID() ) :
        ?>

        <a href="https://wordpress.stackexchange.com/questions/284553/<?php echo get_the_permalink( $latest_post ); ?>"><img src="https://echomartin.com/unit418/wp-content/uploads/2017/10/arrows-last.png" alt="Last"></a>

        <?php
    endif;
endif;
?>

Note that I used $latest_post->ID !== get_the_ID() to check if we were already on the latest post, and to only output the link if we weren’t.