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Hi,

I’m a rising 3L at a T-30. I’m currently doing a SA at a mid size boutique in my specialty area. However, I’m not really happy with the firm. I mentioned that to a big law firm partner who taught a course in my specialty in my school last year. He said his firm would be very interested in me and asked me to email him my resume right away. Do I need to submit a cover letter as well under the circumstances? Please advice.

Kinda.
Don't write and attach a separate cover letter.
But your email should be an actual letter, not just a note that says "See attached." It shouldn't re-introduce yourself to him, since he knows who you are. But it could, briefly, express your interest in the firm and the position, such that, if he forwarded it to a colleague or to HR, they'd know what to do with you.

For example,
"Dear [Partner],
Thank you so much for speaking with me about the opportunity at [law firm] last [Tuesday]. I am very excited about the prospect of working in [law firm's] [litigation] group. [As you know/As we discussed], [another sentence about the group/firm, if you think you have a particularly compelling narrative.] I've attached a resume and transcript, and am happy to provide any additional information you might need.
Thanks again,
[Name]"

Thank you.