Princess in the Emirates briefly inspiring sister (6)
I believe the answer is:
urania
'inspiring sister' is the definition.
(one of the Greek muses)
'princess in the emirates briefly' is the wordplay.
'princess' becomes 'rani' (I've seen this before).
'in' is an insertion indicator.
'the emirates' becomes 'uae' (United Arab Emirates).
'briefly' means to remove the last letter.
'uae' with its final letter taken off is 'ua'.
'rani' placed into 'ua' is 'URANIA'.
(Other definitions for urania that I've seen before include "One of the Muses" , "Muse of astronomy" .)