This character story becomes available in Chapter 3, Episode 3.
Make sure to have Natsu properly equipped and leveled before starting this story. After talking to Gajeel and starting his character story, you’ll be immediately thrown into a 1v1 duel against him. This is a very straightforward match; simply abuse the Crimson Lotus: Fire Dragon Fist to activate Natsu’s Counter stance and just press the Counter prompt to deal more damage. After defeating Gajeel, the quest will be complete and he’ll become a permanent part of the party afterward.
This character story becomes available in Chapter 7, Episode 1.
[-] Ask the guild’s music-lovers for advice.
[-] Go give the items to Gajeel.
After accepting the quest, talk to Mira to get her Sheet Music then find Laxus near the bridge to borrow his music player. Deliver the items to Gajeel to complete the quest. His character rank will increase from 6 to 9 as well.