King's daughter went back inside to get musical instrument (4,5)
I believe the answer is:
reed organ
'musical instrument' is the definition.
(reed organ is a kind of musical instrument)
'king's daughter went back inside' is the wordplay.
'king's daughter' becomes 'Regan' (in Shakespeare's King Lear).
'went' becomes 'rode' (I can't justify this - if you can you should give a lot more credence to this answer).
'back' shows that the letters should be reversed in order.
'inside' indicates putting letters inside.
'rode' in reverse letter order is 'edor'.
'regan' going around 'edor' is 'REED-ORGAN'.
'to get' is the link.
Can you help me to learn more?
(Other definitions for reed organ that I've seen before include "supports traditional services" , "small instrument" , "What you might hear" , "Melody Maker?" , "musical instrument" .)