Popular attraction run by tart (4)
I believe the answer is:
pier
'popular attraction' is the definition.
(as in a pier by the beach)
'run by tart' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'by' is a charade indicator (letters next to each other).
'tart' becomes 'pie' (I've seen this before).
'r' after 'pie' is 'PIER'.
(Other definitions for pier that I've seen before include "Mole, wall between windows" , "Wharf jutting out into water" , "A landing stage or promenade" , "Platform built out from the shore, supported on piles" , "Support member" .)