The author (Fitzgerald) waits until chapter 3 to introduce Gatsby and his use of "this old sport" to create an air of mystery for the reader.
Gatsby's use of the term "this old sport" is an infamous part of his character throughout the story, especially when referring to Nick. His use of this term is introduced together with gatsby in chapter 3.
The author does not introduce Gatsby, the main character of the story, until well into chapter 3 in order to create a sense of mystery for the reader, which is supported by statements describing the unusual nature of the party he was hosting.
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