Lady not running freely sent in for surgery (11)
I believe the answer is:
viscountess
'lady not running' is the definition.
I can't judge whether this defines the answer.
'freely sent in for surgery' is the wordplay.
'freely' is an anagram indicator.
'in' is an insertion indicator.
'for surgery' becomes 'viscous' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'sent' is an anagram of 'ntes'.
'ntes' placed inside 'viscous' is 'VISCOUNTESS'.
Can you help me to learn more?
(Other definitions for viscountess that I've seen before include "title for women" , "aristocrat" , "Noblewoman" .)