Typically they move gold to allies when it’s safer to keep the reserves away (e.g., it’s really hard to imagine the US getting invaded, but that happened to almost all European countries in the last century or so) or when politics become unstable. They take the gold back when the calculus changes. Famously, France got a chunk of its gold back from the US in the 1979s (and finished that process this year).

The rabbit hole goes quite deep: https://en.wikipedia.org/wiki/Gold_repatriation .