“Old sport” is an English term of endearment. Gatsby uses it constantly throughout the novel to bring attention to the short time he spent studying in Oxford (since Oxford is considered a school strictly for “old money”, and Gatsby desperately wants to fit in). But the phrase “old sport” isn’t something that any English person would actually; similar to how Irishmen don’t say “Top o' the mornin'”. This corny phrase highlights that Gatsby doesn’t really understand the way old money works as well as he thinks he does.
To help improve the meaning of these lyrics, visit "The Great Gatsby (Chapter IV)" by F. Scott Fitzgerald and leave a comment on the lyrics box