Second shopping centre not very big (5)
I believe the answer is:
small
'not very big' is the definition.
(big is the opposite of small)
'second shopping centre' is the wordplay.
'second' becomes 's' (common abbreviation).
'shopping centre' becomes 'mall' (a mall is a large shopping complex).
's'+'mall'='SMALL'
(Other definitions for small that I've seen before include "Lower middle of the back" , "Trifle -- half a pint?" , "Minute" , "Of no great size" , "Not great (in number)" .)