Noticed third person with British premier inside drinking establishment (7)
I believe the answer is:
shebeen
'drinking establishment' is the definition.
(I've seen this before)
'noticed third person with british premier inside' is the wordplay.
'noticed' becomes 'seen' (I've seen this in another clue).
'third person' becomes 'he' (I am not sure about this - if you are sure you should believe this answer much more).
'with' means one lot of letters go next to another.
'premier' indicates taking the first letters.
'inside' indicates putting letters inside.
The initial letter of 'british' is 'b'.
'he'+'b'='heb'
'seen' going around 'heb' is 'SHEBEEN'.
Can you help me to learn more?
(Other definitions for shebeen that I've seen before include "place selling hooch" , "Illicit bar in South Africa, Ireland or Scotland" , "still here?" , "Illicit liquor shop" , "Unlicensed drinking den" .)