Linking to a Taxonomy Category

If you go to my homepage:

https://ivyvintage.com/ and under the “Latest Photos” there are some thumbnails. When someone clicks on the image I want them to go to the category of the images post. So for example when someone clicks on the purply coloured shoes I want the link to go to:
https://ivyvintage.com/gallery-category/shoes/

and when clicking on the handbag go to:
https://ivyvintage.com/gallery-category/handbags/

this is what the code looks like to generate the images at the moment:

<li><a href="https://ivyvintage.com/gallery-category/"><img src="<?php echo $recent_project_thumb[0]; ?>" alt="<?php the_title(); ?>" width="162" height="100" class="imgstyle" /></a></li>

Obviously I need to put something in the href section and I have tried everything with no luck. The posts belong to a taxonomy category, this is what functions.php looks like:

register_taxonomy('gallery_cats','gallery',array(
		'hierarchical' => true,
		'labels' => $cat_labels,
		'query_var' => true,
		'rewrite' => array( 'slug' => 'gallery-category' ),
	));

I would really appreciate your help, thank you!