I agree

However, not always the best choice to pick is the best fit.

But consider that this is NOT an official question . As such, I would not hammer my head so much

I believe this question mimic a question from the GRE old big book, with a few tweaks here and there. The answer for that question in the old big book is friend. So ally fits best here.

there is nothing in the question that would suggest that the queen was a cognoscente/connoisseur of the arts. Bestowing patronage to MANY writers and performers simply means supporting them, hence a grand "ally" of the arts would be a better option.

My thoughts exactly! There is no evidence that the Queen is a connoisseur of the arts however there’s clear evidence that she’s an “ally” since she bestows her patronage on and supports them

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The best word to fill the blank is A. connoisseur.

Explanation:
Queen Elizabeth I was known for her patronage and support of the arts, including theater and writers like Shakespeare. Being a "connoisseur" means she was a discerning expert and appreciator of the arts. This fits perfectly with the passage describing her as someone who bestowed patronage and was aptly labeled a grand supporter and appreciator of the arts.
- Critic suggests fault-finding, which doesn't fit the positive context.
- Ally is more general and political, less about arts appreciation.
- Regent means ruler or governor, which she was, but the sentence focuses on arts patronage.
- Judge implies a formal evaluator or decision-maker, less fitting than "connoisseur."

Thus, the sentence reads best as:
"Queen Elizabeth I was quite aptly labeled a grand connoisseur of the arts."