Description of Kane, for example — captain's first in this oddly calm state (7)
I believe the answer is:
citizen
'description of kane for example' is the definition.
(as in the film Citizen Kane)
'captain's first in this oddly calm state' is the wordplay.
'captain's first' becomes 'c' (1st letter of 'captain').
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
'calm state' becomes 'zen' (as in zen meditation).
'in'+'this'='inthis'
The alternating letters of 'inthis' are 'iti'.
'c'+'iti'+'zen'='CITIZEN'
(Other definitions for citizen that I've seen before include "Subject; townsman" , "' - - Kane' (film)" , "Member of community" , "Native or naturalized member of a state" , "One belonging to a specific town or country" .)