Kalai conjectured that every n-vertex r-uniform hypergraph with more than [Formula presented] edges contains all tight r-trees of some fixed size t. We prove Kalai's conjecture for r-uniform hypergraphs that are r-partite. Our result is asymptotically best possible up to replacing the term [Formula presented] with the term [Formula presented]. We apply our main result in graphs to show an upper bound for the Turán number of trees.