A tabloid rejected accepting this compiler's hostility (6)
I believe the answer is:
animus
'hostility' is the definition.
(I know that animosity is a type of enmity)
'a tabloid rejected accepting this compiler's' is the wordplay.
'tabloid' becomes 'sun' (The Sun, UK newspaper).
'rejected' shows that the letters should be reversed in order.
'accepting' means one lot of letters goes inside another (inserted letters are accepted).
'this compiler's' becomes 'im' ('I am' referring to the compiler of the crossword).
'sun' back-to-front is 'nus'.
'nus' placed around 'im' is 'nimus'.
'a'+'nimus'='ANIMUS'
(Other definitions for animus that I've seen before include "Malicious ill-will" , "Hostile feeling" , "A feeling of ill will or hostility" , "Hostility, ill-feeling" , "Hostility shown in speech or action" .)