NY Times almost spreading hatred (6)
I believe the answer is:
enmity
'hatred' is the definition.
(I know that enmity is a type of hatred)
'ny times almost spreading' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'spreading' indicates an anagram.
'ny'+'times'='nytimes'
'nytimes' with its last letter removed is 'nytime'.
'nytime' anagrammed gives 'ENMITY'.
(Other definitions for enmity that I've seen before include "Hostility, ill-will" , "Bad blood" , "ill will" , "Hostility between opposing groups or nations" , "Antagonism, ill-will" .)