Troubled king coherent, losing head (4)

I believe the answer is:

lear

'troubled king' is the definition.
(Shakespeare's King Lear)

I don't understand how the remainder of the clue works.

(Other definitions for lear that I've seen before include "Nonsense poet; drama king" , "Tragic Shakespearean king" , "Lesson" , "British king in play" , "Tragic Shakespearian king" .)

I've seen this clue in The Sun and The Times.

Want a hint initially instead of a full solution? Install my app