There are no bars in Gjógv. The Faroe Islands are broadly dry outside Tórshavn and a handful of larger towns, and Gjógv is a village of fewer than fifty residents with no licensed premises beyond the guesthouse. The Gjáargarður serves coffee and can usually provide a beer or glass of wine to guests; day visitors should not expect a full bar menu.
If you need a drink at the end of the day, the drive back toward Eidi or onward to Tórshavn will take you to better-stocked options.