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In this paper, we prove a definable version of Kirszbraun's theorem in anon-Archimedean setting for definable families of functions in one variable.More precisely, we prove that every definable function $f : X \times Y \to\mathbb{Q}_p^s$, where $X\subset \mathbb{Q}_p$ and $Y \subset \mathbb{Q}_p^r$,that is $\lambda$-Lipschitz in the first variable, extends to a definablefunction $\tilde{f}:\mathbb{Q}_p\times Y \to \mathbb{Q}_p^s$ that is$\lambda$-Lipschitz in the first variable.

Lipschitz extensions of definable p-adic functions