Word for someone who is driven by morality

• righteous

is probably the strongest and most direct

• scrupluous

is another important one

• upstanding
• high-minded

are also venerable terms

Roget's Thesaurus offers the following:

• virtuous
• moral
• upright
• ethical
• honorable
• principled
• honest

Those words may have slightly different connotations, but they all essentially mean that the person is trustworthy because of their moral fiber.

Someone who is zealous about something has a lot of passion for it. Someone who is morally zealous would be someone who is all about sticking to their moral principles:

I really admire her. She truly is a morally zealous person.