What is the "romantic readiness" that the narrator believes Gatsby displays?
That quote needs some context behind it.
"If personality is an unbroken series of successful gestures, then there was something gorgeous about him, some heightened sensitivity to the promises of life.… [Gatsby had] an extraordinary gift for hope, a romantic readiness such as I have never found in any other person and which it is not likely I shall ever find again."
Nick Carraway is describing Gatsby early on in the story. The above quote is a portion of Nick's description. I suppose at first glance a reader could misinterpret "romantic readiness" to mean that Jay Gatsby is ready for some kind of romantic relationship. That would be incorrect. The romantic readiness is describing Gatsby's propensity for being a hopeful dreamer. At his core, Gatsby is an idealist. He believes that if he does all the right moves, then life will sort of just fall into the correct place to most benefit him. He has no reason to doubt this either. He has been very successful so far in life. I mean the guy is loaded with cash. It makes sense that Gatsby has the same optimistic aspirations about Daisy that he did with gaining his wealth. His romantic readiness reflects his shear optimism about the world, his chances with Daisy, his relationship with Nick, etc. It's probably why Nick find Gatsby so fascinating. Nick is a bit of a realistic character, and Gatsby is nothing like that.
Nick Carraway is writing about Gatsby from a sense of deep disillusionment with his fellow humans. He makes a point of distinguishing Gatsby, who "turned out all right at end," from the "foul dust" that "preyed" on Gatsby and soured Nick on "abortive sorrows and short-winded elations of men." Other people have disappointed Nick: Gatsby has not.
In contrast to other people, Gatsby has "romantic readiness" that Nick has never found in anybody else and doesn't expect to ever again. By romantic readiness, Nick means to convey that Gatsby was hopeful, with a "heightened sensitivity to the promises of life." Nick distinguishes this romantic readiness from a creative temperament: Gatsby is not a dreamer who will weave fantasies as an artist might, committing them to a book or a painting. Instead, he is romantic--ready to believe in possibilities, that the world can become what we want it to be--and ready to enact his dreams in real life. Gatsby does everything he can to try to win back Daisy against all the odds, and whether he has won or lost, Nick can't help but admire him for the grand effort he made to realize a dream.