Out-of-date tart filling and spiced tea cold! (7)
I believe the answer is:
archaic
'out-of-date' is the definition.
(thesaurus)
'tart filling and spiced tea cold' is the wordplay.
'filling' says to take the centre (the letters which fill the word).
'and' means one lot of letters go next to another.
'spiced tea' becomes 'chai' (I can't explain this - if you can you should believe this answer much more).
'cold' becomes 'c' (eg on taps).
The centre of 'tart' is 'ar'.
'ar'+'chai'+'c'='ARCHAIC'
Can you help me to learn more?
(Other definitions for archaic that I've seen before include "Very old or old-fashioned" , "Ancient or out of date" , "Obsolete" , "Of a much earlier period" , "Antiquated" .)