Greek character left? Terrible time for a crusade! (10)
I believe the answer is:
pilgrimage
'a crusade' is the definition.
(thesaurus)
'greek character left? terrible time' is the wordplay.
'greek character' becomes 'pi' (letter from the Greek alphabet).
'left?' becomes 'L' (common abbreviation).
'terrible' becomes 'grim' (grim can mean terrible or horrible).
'time' becomes 'age' (an age is a period of time).
'pi'+'l'+'grim'+'age'='PILGRIMAGE'
'for' is the link.
(Other definitions for pilgrimage that I've seen before include "Religiously inspired journey" , "journey to shrine" , "Journey to a sacred place" , "What Chaucer,s travellers were engaged upon" , "special journey?" .)