Can you please tell me if I use this word correctly?

Gallantry:
The hero was ready for the gallantry that came with saving the woman.

No, but he probably displayed gallantry.

So if I changed it to...

The hero displayed gallantry when he saved the woman.

Is that better?

Yes, right.

Yes, you have used the word "gallantry" correctly in your sentence. The word "gallantry" refers to bravery, chivalry, or courageous behavior, especially towards women. In your sentence, you have described how the hero was prepared for the acts of bravery or chivalry that would accompany saving the woman. Well done!