Becoming aware of exhibition centre turning up in swindle (8)
I believe the answer is:
scenting
'becoming aware of' is the definition.
(to scent can mean to learn about or sense)
'exhibition centre turning up in swindle' is the wordplay.
'exhibition centre' becomes 'nec' (National Exhibition Centre).
'turning up' shows that the letters should be reversed in order.
'in' means one lot of letters goes inside another.
'swindle' becomes 'sting' (sting is a kind of swindle).
'nec' backwards is 'cen'.
'cen' put into 'sting' is 'SCENTING'.
(Other definitions for scenting that I've seen before include "Catching the smell of" , "discerning" .)