Hi, I’d be happy if this works for you!
Here are all the necessary codes from my site files. I’ll try to explain where you need to add them all 
First of all, make sure that the ‘Desktop layout’ in the product information section on the product page is ‘Thumbnail Carousel’ (see on the screenshot below; this is in the customization mode of your theme: Admin account menu - Online Store - Themes - Customize) :
Next, go back to Admin account menu - Online Store - Themes - Edit Code.
So, the first code:
{% if section.settings.gallery_layout == 'thumbnail_slider' %} enable_desktop_slider slider--tablet-up {% endif %}
You need to add it to a specific place in the product-media-gallery.liquid file to enable arrows for slider. Here are the screenshots of where I have this code:
Now you need to add a CSS code for your arrows.
Take a look at the screenshots below to see exactly where you need to add it (still in the product-media-gallery.liquid file):
Here’s my code for the arrows on both desktop and mobile:
{% comment %} style start {% endcomment %}
{% comment %} style end {% endcomment %}
In this code, you can also manually change the style settings for the arrow and the circle around it, its border, etc. (I usually just try changing the numbers, watching how it works on the site, and adjust the layout accordingly
)
And finally, I have this code, which also seems to have something to do with these arrows (check first if everything works with the first two, you may not need this one!):
{% if section.settings.gallery_layout == 'thumbnail_slider' %}
{% endif %}
I have it right here:
And now I think that’s it! (as far as I remember, I only added these codes)
Please let me know if this works for you! Good luck! 