Problem in pirouettes after a bad feeling (6)
I believe the answer is:
animus
'bad feeling' is the definition.
(I've seen this before)
'problem in pirouettes after a' is the wordplay.
'problem' becomes 'sum' (arithmetic problem).
'pirouettes' shows that the letters should be reversed in order (I've seen 'pirouetting' mean this (pirouette is a spin in ballet - letters spin round)).
'after' says to put letters next to each other.
'sum'+'in'='sumin'
'sumin' backwards is 'nimus'.
'nimus' put after 'a' is 'ANIMUS'.
(Other definitions for animus that I've seen before include "US man I turn to with hostility" , "Hostility, bad feeling toward" , "A feeling of ill will or hostility" , "Heat" , "Motivating spirit" .)