Kind of word that either part of down clue can be, never across (4)
I believe the answer is:
verb
I believe this is a double definition.
'kind of word' is the first definition.
(verb is a type of word)
'that either part of down clue can be never across' is the second definition.
('down' and 'clue' are verbs, but 'across' is not)
(Other definitions for verb that I've seen before include "Predicate of a sentance (4)" , "Word that denotes an action or a state" , "Maybe protest" , "love, for example" , "Part of speech" .)