Dog, note, by entrance to Downing Street, barking (3,6)
I believe the answer is:
red setter
'dog' is the definition.
(red setter is a kind of dog)
'note by entrance to downing street barking' is the wordplay.
'note' becomes 're' (**).
'by' says to put letters next to each other.
'entrance to' suggests taking the first letters.
'barking' indicates anagramming the letters (UK slang for mad).
The first letter of 'downing' is 'd'.
'street' anagrammed gives 'setter'.
're'+'d'+'setter'='RED SETTER'
(Other definitions for red setter that I've seen before include "one identifying the game" , "Shepherds are delighted to see this" , "Pet" , "Gun dog" , "supplier of crosswords to the Daily Worker?" .)