How to set a post featured image from an already made custom field

Question

Your question is not entirely clear, but I suppose your new theme is using featured images in the normal way, which leaves empty featured images on older posts, because they are stored in a custom field. You can catch those using the filter at the end of get_the_post_thumbnail. Because I don’t know how the custom field is made I can’t give complete code, but it would look like this:

add_filter ('post_thumbnail_html','wpse303106_custom_featured_image',10,5);

function wpse303106_custom_featured_image ($html, $post->ID, $post_thumbnail_id, $size, $attr) {
  if ('' == $html && test-for-existence-of-custom-field) {
    $html = ... assemble from custom field ...
    }
  return $html;
  }