Looking around the outskirts of Tintagel is surprising (9)
I believe the answer is:
startling
'is surprising' is the definition.
('startling' can be similar in meaning to 'surprising')
'looking around the outskirts of tintagel' is the wordplay.
'looking' becomes 'staring' (staring is a kind of looking).
'around' is an insertion indicator.
'the outskirts of' means to remove the middle letters.
'tintagel' with its middle removed is 'tl'.
'staring' going around 'tl' is 'STARTLING'.
(Other definitions for startling that I've seen before include "Causing shock" , "Producing sudden alarm" , "Rattlings of alarming kind" , "Astonishing or shocking" , "Suddenly frightening" .)