Why is Klipspringer, whom we meet in Chapter 5 of The Great Gatsby, important?
Nick describes Ewing Klipspringer as:
...an embarrassed, slightly worn young man, with shell-rimmed glasses and scanty blond hair. He was now decently clothed in a sport shirt, open at the neck, sneakers and duck trousers of a nebulous hue.
Klipspringer is "embarrassed" because he has made himself an uninvited permanent house guest. Perhaps he didn't think that Gatsby knew he was there. He must be broke and unemployed, sponging off Gatsby.
Gatsby summons Klipspringer ostensibly to play the piano for them, and the young freeloader plays the popular 1920's tune "Ain't We Got Fun?" But the real function of this minor character is to serve as a sort of chaperone. Nick is going to leave Gatsby and Daisy alone at the end of Chapter V. Nick was Daisy's escort up to that point. Otherwise it would have been improper, by the standards of the time, to leave Daisy alone like that. It would have been too obvious why Gatsby had invited them over and what was going to happen. But with Klipspringer present, Daisy and Gatsby are not quite alone, and Nick can make his departure (a departure which both Daisy and Gatsby obviously want) without seeming to abandon his role as Daisy's escort. This is a sensitive moment because Nick is so conspicuously being placed in the role of pander, go-between, entremetteur.
It is noteworthy that, although there are two affairs going on throughout the novel, there is never any explicit description of intimate physical contact. The end of Chapter V is like one of those "fade outs" Hollywood used to employ in the days when the movie censors would not permit anything more than kissing on the screen. After Klipspringer appears and starts playing the piano, Nick politely "fades out" as gracefully as possible under the circumstances. These are the last words in Chapter V.
They had forgotten me, but Daisy glanced up and held out her hand. Gatsby didn't know me now at all. I looked once more at them and they looked back at me, remotely possessed by intense life. Then I went out of the room and down the marble steps into the rain, leaving them there together.
What happens after that is left to the reader's imagination. Gatsby undoubtedly gets rid of Klipspringer very quickly after Nick's departure.
In Chapter VII there will be a telephone conversation in which Nick says to Gatsby:
"I hear you fired all your servants."
"I wanted somebody who wouldn't gossip. Daisy comes over quite often--in the afternoons."