This function will help to show links in wordpress excerpt.

html_link_in_excerpt.php

<?php
function keep_my_links($text) {
  global $post;
if ( '' == $text ) {
    $text = get_the_content('');
    $text = apply_filters('the_content', $text);
    $text = str_replace('\]\]\>', ']]&gt;', $text);
    $text = preg_replace('@<script[^>]*?>.*?</script>@si', '', $text);
    $text = strip_tags($text, '<a>');
  }
  return $text;
}
remove_filter('get_the_excerpt', 'wp_trim_excerpt');
add_filter('get_the_excerpt', 'keep_my_links');
?>