Link prediction is a common problem in network science that transects many disciplines. The goal is to forecast the appearance of new links or to find links missing in the network. Typical methods for link prediction use the topology of the network to predict the most likely future or missing connections between a pair of nodes. However, network evolution is often mediated by higher-order structures involving more than pairs of nodes; for example, cliques on three nodes (also called triangles) are key to the structure of social networks, but the standard link prediction framework does not directly predict these structures. To address this gap, we propose a new link prediction task called "pairwise link prediction" that directly targets the prediction of new triangles, where one is tasked with finding which nodes are most likely to form a triangle with a given edge. We develop two PageRank-based methods for our pairwise link prediction problem and make natural extensions to existing link prediction methods. Our experiments on a variety of networks show that diffusion based methods are less sensitive to the type of graphs used and more consistent in their results. We also show how our pairwise link prediction framework can be used to get better predictions within the context of standard link prediction evaluation.