One running a Scottish island (4)
I believe the answer is:
iona
'scottish island' is the definition.
(island of the Hebrides)
'one running a' is the wordplay.
'one' becomes 'i' (Roman numeral).
'running' becomes 'on' (eg when a machine is running it is on).
'i'+'on'+'a'='IONA'
(Other definitions for iona that I've seen before include "Isolated part of UK" , "St Columba's monastery isle" , "inch" , "Scots monastery isle" , "island off Scotland" .)