Hate getting tips from arithmetician: one’s useless! (6)
I believe the answer is:
animus
'hate' is the definition.
(animus is a kind of hate)
'tips from arithmetician one's useless' is the wordplay.
'tips from' suggests removing the centre.
'one's' becomes 'I'm' ('one is' is a formal way of saying 'I am').
'useless' becomes 'us' (abbreviation for unserviceable).
'arithmetician' with its middle taken out is 'an'.
'an'+'im'+'us'='ANIMUS'
'getting' acts as a link.
(Other definitions for animus that I've seen before include "Heat" , "Bad blood" , "A feeling of ill will or hostility" , "Feeling of strong dislike" , "US man I turn to with hostility" .)