Detective left picture taken after Greek expedition (10)
I believe the answer is:
pilgrimage
'expedition' is the definition.
(thesaurus)
'detective left picture taken after greek' is the wordplay.
I cannot really see how this works, but
'detective' could be 'pi' (private investigator) and 'pi' is located in the answer.
'left' could be 'l' (common abbreviation) and 'l' is found within the answer.
'picture' could be 'image' (synonyms) and 'image' is found within the answer.
'greek' could be 'gr' (abbreviation for Greek) and 'gr' is found in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for pilgrimage that I've seen before include "Religiously-inspired journey" , "Journey to a sacred place" , "Holy journey" , "Religiously inspired journey" , "journey to shrine" .)