You Do Need power plug adapter while traveling from Gibraltar to Faroe Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K and in Gibraltar is G. This is how they look like.

Gibraltar

In Gibraltar, outlets of type G are in use.

Type G

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K