Finish off next article (3)
I believe the answer is:
the
'article' is the definition.
(the 'definite article' part of speech)
'finish off next' is the wordplay.
'finish off' means to remove the last letter.
'next' becomes 'then' (I've seen this before).
'then' with its final letter removed is 'THE'.
(Other definitions for the that I've seen before include "See 10 Across" , "Base of ever-expanding nursery rhyme" , "Finis" , "and 24 Down: Similar things" , "Over - - moon" .)