Oddly sick niece possibly requires discipline (7)
I believe the answer is:
science
'discipline' is the definition.
(science is a kind of discipline)
'oddly sick niece possibly' is the wordplay.
'oddly' means one should take alternating letters (letters in odd-numbered positions).
'possibly' indicates anagramming the letters.
The alternating letters of 'sick' are 'sc'.
'niece' with letters rearranged gives 'ience'.
'sc'+'ience'='SCIENCE'
'requires' is the link.
(Other definitions for science that I've seen before include "Academic discipline" , "Study of physical things by observation and experiment" , "Biology, for example" , "something learnt at school" , "Technology" .)