Club next to apartment that’s used to press (8)
I believe the answer is:
flatiron
'used to press' is the definition.
(a flatiron presses clothes)
'club next to apartment' is the wordplay.
'club' becomes 'iron' (type of golf club).
'next to' is a charade indicator (letters next to each other).
'apartment' becomes 'flat' (synonyms).
'iron' after 'flat' is 'FLATIRON'.
'that's' is the link.
(Other definitions for flatiron that I've seen before include "Old-fashioned clothes presser" , "Fire-heated smoother" , "Old device for pressing clothes" , "Latin for (anag) - old domestic appliance" , "Antique household implement" .)