Tyneside area containing popular square (4)
I believe the answer is:
nine
'square' is the definition.
(I've seen this before)
'tyneside area containing popular' is the wordplay.
'tyneside area' becomes 'ne' (North East of England**).
'containing' is an insertion indicator.
'popular' becomes 'in'.
'ne' placed around 'in' is 'NINE'.
(Other definitions for nine that I've seen before include "Cat's lives? - the next clue?" , "Number IX" , "A number of worthies" , "Number of the ancient Muses" , "Figure" .)