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Usual networks lossily (if not incorrectly) represent higher-order relations, i.e. those between multiple entities instead of a pair. This calls for complex structures such as hypergraphs to be used instead. Akin to the link prediction problem in graphs, we deal with hyperlink (higher-order link) prediction in hypergraphs. With a handful of solutions in the literature that seem to have merely scratched the surface, we provide improvements for the same. Motivated by observations in recent literature, we first formulate a "clique-closure" hypothesis (viz., hyperlinks are more likely to be formed from near-cliques rather than from non-cliques), test it on real hypergraphs, and then exploit it for our very problem. In the process, we generalize hyperlink prediction on two fronts: (1) from small-sized to arbitrary-sized hyperlinks, and (2) from a couple of domains to a handful. We perform experiments (both the hypothesis-test as well as the hyperlink prediction) on multiple real datasets, report results, and provide both quantitative and qualitative arguments favoring better performances w.r.t. the state-of-the-art.