Royal duets are unusually highly valued (9)
I believe the answer is:
treasured
'highly valued' is the definition.
'treasured' can be an answer for 'valued' (I've seen this before). I am not certain of the 'highly' bit.
'royal duets are unusually' is the wordplay.
'royal' becomes 'r' (common abbreviation e.g. RM - Royal Marine).
'unusually' indicates an anagram.
'r'+'duets'+'are'='rduetsare'
'rduetsare' with letters rearranged gives 'TREASURED'.
Can you help me to learn more?
(Other definitions for treasured that I've seen before include "Chersihed, held dear" , "Cherished, held dear" , "Darling" , "Valued" , "thought highly of" .)