Gradually introduce in street first signs of improvements locally (6)
I believe the answer is:
instil
'gradually introduce' is the definition.
'in street first signs of improvements locally' is the wordplay.
'street' becomes 'st' (abbreviation).
'first signs of' indicates taking the first letters.
The initial letters of 'improvements locally' is 'il'.
'in'+'st'+'il'='INSTIL'
(Other definitions for instil that I've seen before include "Inculcate" , "Implant (in the mind)" , "Introduce into mind, being in list" , "Mentally fix" , "It's nil (anag.)" .)