Island finally finishes link by bridge (4)
I believe the answer is:
skye
'island' is the definition.
(Scottish island)
'finally finishes link by bridge' is the wordplay.
'finally' indicates one should take the final letters.
The final letters of 'finishes link by bridge' are 'SKYE'.
(Other definitions for skye that I've seen before include "Large Scottish island" , "Scotland island" , "Where Bonnie Prince Charlie fled after his defeat at Culloden" , "Hebridean island close to mainland" , "Largest isle of the Inner Hebrides" .)