Sure did. Luffy overcame many challenges and ultimately emerged victorious against Kaido. It was a long and hard-fought struggle that showcased Luffy's growth and determination.
Luffy beats Kaido by unlocking new powers and exploiting Kaido's weaknesses. He also gains support from his allies and uses teamwork to his advantage. The battle is intense and filled with unexpected twists.
I don't have enough context to determine exactly who 'garp' is. It could be a newly created character by the fanfic writer, or it might be a character from a relatively unknown story that is being incorporated into the 'ace fanfic'.
You could start by looking on popular fanfiction websites like Archive of Our Own (AO3) or FanFiction.net. They have a large collection of fan - created works and there's a good chance you might find 'garp save ace fanfiction' there.