Let $k$ be a field equipped with a complete and non-archimedean absolute value $|\raisebox{1.72218pt}{.}|$ (which could be trivial). Let $X$ be a projective scheme over $\operatorname{Spec}k$ and $L$ be an ample invertible sheaf on $X$, equipped with a continuous and semi-positive metric $|\raisebox{1.72218pt}{.}|_{h}$. Let $Y$ be a closed subscheme of $X$ and $l\in H^{0}(Y,L|_{Y})$. For any $\epsilon>0$ there exists an integer $n_{0}\geq 1$ such that, for any integer $n\geq n_{0}$, the section $l^{\otimes n}$ extends to a section $s\in H^{0}(X,L^{\otimes n})$ verifying $\|s\|_{h}\leq{e}^{\epsilon n}\|l\|_{Y,h}^{n}$.