My personal opinion is that it’s rude to single out composers for their biology. Let’s keep it about the music, yeah? I would say these next two are part of the greats, not just standing with them:

Hildur Guðnadóttir for the amazing scores on Chernobyl and Joker Mica Levi (non-binary) for Under the Skin and Jackie

So the "greats" are all film composers?

Weird, but even if you're limiting it that way, how about Hildur Guðnadóttir?

And if it's not weirdly limited to soundtracks, then you've got Jennifer Higdon, Kaija Saariaho, Unsuk Chin ...

Well, I'm sorry. When it comes to composers, past and present, no woman comes to mind. I'm just looking for some.

And whose fault is that?

Why would this be downvoted? Weird.

There are plenty. Sure, the canon is full of males, but that's just a function of the canon itself.

Is it a fault if they are actively seeking your help to correct it?

Yoko Kanno!

Also, I always loved Shirley Walker on Batman The Animated Series.

Punchy, appropriate, custom composed to the beats of each scene, surprisingly varied. Very talented.

I gave my answer and they said “no woman comes to mind”, not “I know some great composers who are women and would like to learn about others”

Because none genuinely came to my mind.

Plenty of phenomenal female composers in the classical music world. Since you've listed a bunch of film composers, someone like Caroline Shaw or Libby Larsen might be up your street.

The idea of the "Greats" is a bit of an interesting concept anyway; speaking as a classical musician, the idea of the Canon that I grew up with was actually really only constructed in the early 20th century within academia as a way of presenting a narrative structure of music history that really centered Germanic music. A lot of who we think of as the "Greats" of a particular era often were not seen that way during their time at all; Bach was of course famously forgotten until Mendelssohn found his manuscripts in Leipzig and began a revival of his music. Mendelssohn himself was considered world class during his lifetime, but when Wagner wrote his treatise attacking Jews in Music (and specifically named Mendelssohn for having Jewish ancestry), Mendelssohn was removed from being thought of as one of the "Greats."

Anyway, I say all that because there were a ton of successful, popular women composers who were considered first rate in their time that were purposely omitted when the Canon was being constructed. Florence Price, Ethyl Smyth, Amy Beach, and Rebecca Clarke were all very highly regarded in the late Romantic Era; Price has been having a pretty big resurgence the last few years, actually.

But yeah, sorry for the long post. Check out Shaw, Larsen, and Jennifer Higdon. Sofia Gubaidalina and Kaijia Saariaho if youre up for something a bit crunchier. But for real, there are so many out there that we in the classical music world are finally starting to try and recognize.