Problem in a rising display of hostility (6)
I believe the answer is:
animus
'display of hostility' is the definition.
'problem in a rising' is the wordplay.
'problem' becomes 'sum' (arithmetic problem).
'rising' shows that the letters should be reversed in order (going up in a down clue).
'sum'+'in'+'a'='sumina'
'sumina' back-to-front is 'ANIMUS'.
(Other definitions for animus that I've seen before include "Motivating spirit" , "spirit of hostility" , "US man I turn to with hostility" , "Hostile feeling" , "Bad blood" .)