How to get a taxonomy custom image field URL value
In Drupal images are File entities, the target_id is the File ID. So...

$fid = $field-&gt;getValue()[0]['target_id']; // File ID, 

// Note the [0] in the array. We assume there is always going to be 1 image here. 
// If your field allows more than 1 image, you will need to loop through each $field-&gt;getValue()

$file = \Drupal\file\Entity\File::load($fid); // load File entity object

$file_url = $file-&gt;url(); // get the URL.