Annoying by looking around the street (9)
I believe the answer is:
pestering
'annoying' is the definition.
(I know that annoying can be written as pestering)
'looking around the street' is the wordplay.
'looking' becomes 'peering' (peering is a kind of looking).
'around' indicates putting letters inside.
'the street' becomes 'st' (abbreviation).
'peering' enclosing 'st' is 'PESTERING'.
'by' is the link.
(Other definitions for pestering that I've seen before include "Annoying persistently" , "Annoying constantly" .)