What is a fresh renaming?

Given a set of variables $𝒳$, a set of sorts $𝒮$, a sort-indexed family of $𝒜=\{{𝒜}_s\}$, then a Fresh renaming relative to $𝒳$ is a bijection $\rho :\overrightarrow{x}\leftrightarrow {\overrightarrow{x}}^{\prime }$, such that $\overrightarrow{x}\notin 𝒳$.