Its monarch (female, with an arts degree) was very ancient (5)
I believe the answer is:
sheba
'arts degree was very ancient' is the definition.
I can't tell whether this definition defines the answer.
'its monarch female with an' is the wordplay.
I cannot quite see how this works, but
'female' could be 'she' ('she' refers to a woman) and 'she' is found in the answer.
'an' could be 'a' and 'a' is present in the answer.
A single letter 'b' remains which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for sheba that I've seen before include "Old South Arabian kingdom" , "Ancient Kingdom of the Sabeans" , "Ancient name of South Yemen" , "OT Queen" , "Its queen arrived" .)