The most significant person would probably have to be Leonard Peikoff, the author of Objectivism: The Philosophy of Ayn Rand. The book's writing was supervised and authorized by Ayn Rand, but Peikoff provided a structure and clarity to Objectivism that Ayn Rand never did on paper.
Ayn Rand's work exists spread across op-eds, articles, and speeches. The fiction merely gives you "a feel for" what she was trying to communicate. Leonard Peikoff, by authoring this book, delivered a cumulative presentation from start to finish of the entire body of Objectivist thought.
A lot of people don't view this as significant. The significance of this book is that it presents Objectivism as an integrated interdependent hierarchical conceptual unit (as it was intended). If you flip to page 200 and begin reading about a topic, pages 1-199 are required reading because the contents on page 200 depend upon every concept in the preceding pages. Peikoff also adds a level of linguistic finesse through examples and metaphors that Ayn Rand never could because she wasn't born a native English speaker. Peikoff's ability to help the reader conceptualize with reference to Ayn Rand's work greatly helps the reader organize and structure the conceptual framework to continue onward through the book to more complex higher level concepts.
Another important work that developed on the economic theory in Rand's work is The Capitalist Manifesto by Andrew Bernstein. This book went mostly under the radar despite its alluring title. (As opposed to the widespread media coverage of the recent critique of Capitalism Capital in the Twenty First Century, by Thomas Piketty).
In the realm of cognition, the second edition of Introduction to Objectivist Epistemology includes an essay from Leonard Peikoff on the Analytic-Synthetic Dichotomy that is worth reading.
More recently attempts have been made to show that Objectivism was never meant to be presented as cultivaing and promoting hordes of "Nietzschean monsters who couldn't spare a dime for a tramp" with David Kelley's Unrugged Individualism: The Selfish Basis of Benevolence. This is important because often critics of Objectivism dehumanize Objectivists as unfeeling hyper-rational "Randroids" who stick out like a sore thumb in society (literally nobody in my personal or professional life knows of my admiration of Ayn Rand).
There are also thinkers that are loosely compatible with Objectivism, but you would probably never find one of the leading Objectivist intellectuals (Leonard Peikoff, Yaron Brook, Harry Binswanger) endorsing them.
Thinkers aligned with the Austrian School of economics are also ideologically compatible with Objectivism. Compatible in the sense that these theories can easily be "embedded" within the overall Objectivist ethical and political frameworks very easily. They do the best job of describing the "nuts and bolts" of the kind of Capitalism that Objectivism prescribes. While not explicitly contributing to Objectivism philosophically, Austrian economics gives you the case for how markets work practically, while Objectivism gives you their broader justification ethically. I would recommend Capitalism: A Treatise on Economics by George Reisman, as well as the essential Rothbard and Mises.
Authors who have written on the subject of Atheism are also aligned with Objectivism insofar as they offer specific arguments for discarding supernatural faith-based thinking in favor of Reason and Science. In George H. Smith's Atheism: The Case Against God he actually references Ayn Rand's method of concept formation several times in his conceptual formulation for what Atheism is. Other examples include the more recent "Four Horsemen of Atheism" (Richard Dawkins, the late Christopher Hitchens, Dan Dennett, and Sam Harris) offer a lot as well while none explicitly advocate Objectivism.
A disclaimer is in order I think. It must be understood that the authors mentioned as merely "compatible" would have more than likely been regarded as incompatible by Ayn Rand because these thinkers often do not integrate their well reasoned arguments into a broader conceptual framework presented as a whole.
