Old monarch’s new name in doubt (5,4)
I believe the answer is:
queen mary
'old monarch's' is the definition.
(I know that Queen Mary is a queen regnant)
'new name in doubt' is the wordplay.
'new' is an anagram indicator.
'in' means one lot of letters goes inside another.
'doubt' becomes 'query' (a query is a doubt or question).
'name' with letters rearranged gives 'enma'.
'enma' placed into 'query' is 'QUEEN MARY'.
(Other definitions for queen mary that I've seen before include "Famous old ocean liner now in California" , "Cunard's flagship when launched in 1934" .)