Green Arrow was at a career low during the period 1964 – 1967: the New Look. His back-up series had ended, and the archer was reduced to sporadic appearances in the pages of Justice League of America. Although he had no solo stories during this era, Green Arrow did team up with Batman in the pages of Brave and the Bold 71. There was no development of the archer in that story, alas, and Speedy did not appear in it. Although nothing was made of it until the 70s, the split between Green Arrow and his ward effectively began during this era.
The story is not a great one. It deals with two rivals for the leadership of the Kijowa tribe. The good one looks to Batman and Green Arrow for mentorship in the skills needed to win the competition, while the bad one bribes the promoter to rig the contest. There is an uncomfortably racist element in the good native needing training by white men to triumph in this contest to become the chief of his tribe, although fortunately never gets made explicit. The bad one wins, with the aid of the promoter. The promoter was really after the secret of the Thunderbird, and forces the guy to reveal it. They bring the legendary Thunderbird to life, and of course it goes out of control. Batman and Green Arrow are needed to subdue the creature. Once again, white men are needed to solve the problems of the natives, and the one they have "endorsed" becomes the chief at the end of the story.
Green Arrow continues in the next period, 1967 – 1969: It’s a Happening!
Green Arrow: Brave and the Bold 71 (April/May 1967)