Support for bridge is in the morning — it’s an old thing (8)
I believe the answer is:
archaism
'an old thing' is the definition.
(something archaic or outdated)
'support for bridge is in the morning' is the wordplay.
'support for' is a charade indicator (letters next to each other) (in a down clue, some letters 'support' others).
'bridge' becomes 'arch' (I've seen this before).
'in the' means one lot of letters goes inside another.
'morning' becomes 'am' (as in 12:00 AM).
'is' going into 'am' is 'aism'.
'arch'+'aism' is 'ARCHAISM'.
'it's' acts as a link.
(Other definitions for archaism that I've seen before include "Outmoded term" , "Old-fashioned expression" , "Something outdated" , "Charisma (anag) - something very old-fashioned" , "Out-of-date word" .)