Taking back right to rise up in response (10)
I believe the answer is:
retraction
'taking back' is the definition.
(to retract is to take something back)
'right to rise up in response' is the wordplay.
'right' becomes 'r' (common abbreviation).
'to' means one lot of letters go next to another (I've seen this in other clues).
'rise up' becomes 't' (I can't justify this - if you can you should give a lot more credence to this answer).
'in' indicates putting letters inside.
'response' becomes 'reaction' ('reaction' can be a synonym of 'response').
'r' put after 't' is 'tr'.
'tr' placed into 'reaction' is 'RETRACTION'.
(Another definition for retraction that I've seen is " Withdrawal of a statement".)