Leave unfinished line about king being eccentric (6)
I believe the answer is:
quirky
'eccentric' is the definition.
(thesaurus)
'leave unfinished line about king' is the wordplay.
'leave unfinished' becomes 'qui' (I can't justify this - if you can you should give a lot more credence to this answer).
'line' becomes 'ry' (abbreviation for railway).
'about' means one lot of letters goes inside another.
'king' becomes 'k'.
'ry' enclosing 'k' is 'rky'.
'qui'+'rky'='QUIRKY'
'being' is the link.
(Other definitions for quirky that I've seen before include "Idiosyncratic" , "'Kinky, off-beat (6)'" , "Peculiar in behaviour" .)