Hi Olga,
It sounds ok to say "members of the nobility all wanted portraits made by her", but in my opinion you would say it this way if you wanted to emphasise the word 'her', in relation to another person.
However, the sentence you wrote makes it unclear who you are talking about.
"As a consequence of the Queen’s patronage, she became more and more popular and members of the nobility all wanted portraits made by her". - in this sentence it sounds as though you are talking only about the queen, and that the queen is the portrait maker.
It might be better to say ""As a consequence of the Queen’s patronage, the woman artist became more and more popular and members of the nobility all wanted portraits made by her".
I hope this helps!