Middlesex possibly is holding trade fair (4)
I believe the answer is:
expo
'trade fair' is the definition.
(I've seen this in another clue)
'middlesex possibly is holding' is the wordplay.
'is holding' indicates a hidden word.
'EXPO' is hidden in the letters of 'middlesex possibly'.
(Other definitions for expo that I've seen before include "World fair, e.g. Seville 1992" , "Show" , "Major international fair" , "Public showing" , "Trade fair" .)