Danish prince losing head about king’s band (6)
I believe the answer is:
armlet
'king's band' is the definition.
'armlet' can be an answer for 'band' (armlet is a kind of band). I'm not sure about the 'king's' bit.
'danish prince losing head about' is the wordplay.
'danish' becomes 'r' (I can't justify this - if you can you should give a lot more credence to this answer).
'prince' becomes 'hamlet' (Prince of Denmark in Shakespeare's Hamlet).
'losing head' means to remove the first letter.
'about' is an insertion indicator.
'hamlet' with its first letter taken off is 'amlet'.
'r' placed within 'amlet' is 'ARMLET'.
Can you help me to learn more?
(Other definitions for armlet that I've seen before include "Martel (anag.)" , "Band worn for decoration" , "Small band" , "brassard" , "Elm rat (anag)" .)