Print taxonomy term description onto product page I am currently running Drupal Commerce 7.

The products listed are all referenced to different designers through a "Designer" Taxonomy.
Within the Taxonomy, the individual terms, i.e. the different designers have an added description. I would like to know if there is any way to print on the product page the description for the particular designer referenced by the page. 

For instance I have a shoe. I have it designed by Mary under "Designer". I have also attached an example description for Mary: "Mary is a great designer". I would like to print this somehow onto the product page.
It depends a lot on how you're showing this page/information, most probably you're using Views lo list these products, so you can add a Relationship from the Product entity to the Taxonomy (from product variation or display, doesn't matter) to show the fields coming from your categories.

If it's in the product page, it might get trickier, I'd use Display Suite to show fields from other entities, Dynamic fields is an option included in DS and alows you to explore more information that is available for display contextually on your current entity view mode.