The actor can be seen celebrating his 37th birthday with cast members such as Sarah Laine at Rose Street Garden on George Street.
Featured in the Rose Street Garden’s ‘pics of the week’ on Facebook, the star and fellow cast members can be seen enjoying drinks in the cocktail garden and posing beside their popular Instagram photo op Telephone Box.
In their post, Rose Street Garden said: “Another amazing week at RSG with some familiar faces visiting whilst filming in the capital.
"Thanks again to everyone for your support and remember we are open INDOORS from next Monday at The Secret Garden.”
Mr Compston and the rest of the cast are currently staying in Edinburgh as filming for the The Rig takes place.