functions.php

<?php
// add yearly archives for custom post type
function custom_post_rewrite( $rewrite_rules ) {
  $pagination_base = $GLOBALS['wp_rewrite']->pagination_base;
  $slug = 'cpt slug goes here';

  $year_archive = array(
    $slug . '/([0-9]{4})/' . $pagination_base . '/?([0-9]{1,})/?$' => 'index.php?post_type=' . $slug . '&year=$matches[1]&paged=$matches[2]',
    $slug . '/([0-9]{4})/?$' => 'index.php?post_type=' . $slug . '&year=$matches[1]',
  );
  $rewrite_rules = $year_archive + $rewrite_rules;
  return $rewrite_rules;
}
add_filter('rewrite_rules_array', 'custom_post_rewrite');