Greatest hunger is in Paris (7)
I believe the answer is:
longest
'greatest' is the definition.
'hunger is in paris' is the wordplay.
'hunger' becomes 'long' (both can mean to crave).
'is in paris' becomes 'est' ('is' in French).
'long'+'est'='LONGEST'
(Other definitions for longest that I've seen before include "Of greatest duration" , "Having the most length" , "For the most time" , "Least short" , "Extending farthest" .)