A digraph D is k-linked if for any pair of two disjoint vertex sets \(\{x_{1},x_{2},\ldots ,x_{k}\}\) and \(\{y_{1},y_{2},\ldots ,y_{k}\}\) in D, there exist vertex disjoint dipaths \(P_{1},P_{2},\ldots ,P_{k}\) such that \(P_{i}\) is a dipath from \(x_{i}\) to \(y_{i}\) for each \(i\in [k]\) . Pokrovskiy (JCTB, 2015) confirmed a conjecture of Kühn et al. (Proc. Lond. Math. Soc., 2014) by verifying that every 452k-connected tournament is k-linked. Meng et al. (Eur. J. Comb., 2021) improved this upper bound by showing that any \((40k-31)\) -connected tournament is k-linked. In this paper, we show a better upper bound by proving that every \(\lceil 12.5k-6\rceil \) -connected tournament with minimum out-degree at least \(21k-14\) is k-linked. Furthermore, we improve a key lemma that was first introduced by Pokrovskiy (JCTB, 2015) and later enhanced by Meng et al. (Eur. J. Comb., 2021).
