Traveller sees Prime Minister hugging single girl, shaken (7)
I believe the answer is:
pilgrim
'traveller' is the definition.
(pilgrim is a kind of traveller)
'prime minister hugging single girl shaken' is the wordplay.
'prime minister' becomes 'pm' ('PM' can be a synonym of 'prime minister').
'hugging' means one lot of letters goes inside another.
'single' becomes 'i' (one).
'shaken' is an anagram indicator.
'i'+'girl'='igirl'
'igirl' with letters rearranged gives 'ilgri'.
'pm' placed around 'ilgri' is 'PILGRIM'.
'sees' acts as a link.
(Other definitions for pilgrim that I've seen before include "One on journey to shrine" , "traveller wanting to visit shrine" , "made progress, as booked" , "these early Fathers" , "... emigrants to Massachusetts" .)