Constant parking problem in streets (10)
I believe the answer is:
persistent
'constant' is the definition.
(thesaurus)
'parking problem in streets' is the wordplay.
'parking' becomes 'p' (abbreviation on road signs).
'problem' indicates an anagram.
'in'+'streets'='instreets'
'instreets' is an anagram of 'ersistent'.
'p'+'ersistent'='PERSISTENT'
(Other definitions for persistent that I've seen before include "Not taking "no" for an answer" , "Ongoing" , "Resolute - interminable" , "Lasting, prolonged" , "Prolonged; nagging" .)