You Do Need power plug adapter while traveling from Cyprus 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 Cyprus is G. This is how they look like.

Cyprus

In Cyprus, 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