Clue: Scots departed to visit part of Guernsey, an island state (7)
Answer: SARAWAK
Explanation: Definition: an island state
**AWA** ("Scots" for "departed") *to visit* **SARK** ("part of Guernsey") 
Sark forms part of the bailiwick of Sark, and Sarawak is a state of Malaysia on an island (Borneo) rather than an "island state" which I think is a "state made up of one or more islands".