Island providing some inspiration, ascetically (4)
I believe the answer is:
iona
'island' is the definition.
(I've seen this before)
'some inspiration ascetically' is the wordplay.
'some' indicates the answer is hidden within the clue (some of the parts of the word are used).
'IONA' can be found hidden inside 'inspiration ascetically'.
'providing' acts as a link.
(Other definitions for iona that I've seen before include "Macbeth's resting" , "inch" , "early Christian centre" , "Inner Hebridean island" , "Island west of Mull" .)