Nieces running around could face discipline (7)
I believe the answer is:
science
'discipline' is the definition.
(I know that science is a type of discipline)
'nieces running around could face' is the wordplay.
'running' is an anagram indicator (the letters run around to different places).
'around' indicates putting letters inside.
'face' suggests taking the first letters.
The first letter of 'could' is 'c'.
'nieces' is an anagram of 'sience'.
'sience' going around 'c' is 'SCIENCE'.
(Other definitions for science that I've seen before include "Subject such as biology, physics, etc" , "Christian --; -- fiction" , "Physics or chemistry, say" , "Eg, botany or physics" , "Specialised knowledge" .)