One nurse could possibly like sceptical people? (11)
I believe the answer is:
incredulous
'like sceptical people?' is the definition.
(incredulous means sceptical or disbelieving)
'one nurse could possibly' is the wordplay.
'one' becomes 'I' (Roman numeral).
'possibly' indicates an anagram.
'nurse'+'could'='nursecould'
'nursecould' is an anagram of 'ncredulous'.
'i'+'ncredulous'='INCREDULOUS'
(Other definitions for incredulous that I've seen before include "Unable to believe something" , "Unwilling to believe something" , "Sceptical, unbelieving" .)