Most desolate quarter has listed building (7)
I believe the answer is:
wildest
'most desolate' is the definition.
('wild' can be a synonym of 'desolate')
'quarter has listed building' is the wordplay.
'quarter' becomes 'w'.
'has' says to put letters next to each other.
'building' indicates an anagram.
'listed' with letters rearranged gives 'ildest'.
'w'+'ildest'='WILDEST'
(Other definitions for wildest that I've seen before include "Least tame" , "Most untamed" , "Most crazy" , "Least disciplined" .)