A private banker moves firms. They retain, formally or not, knowledge of their book. The client whose affairs were known to one institution becomes, in some measure, a topic of conversation at another. Regulators have rules about this; the rules slow the leak; they do not prevent it.
The detail that travels is not usually account numbers or balances. It is more useful than that: who the principal is, what kind of money they have, who advises them, what they tend to invest in, what they have asked about recently. This kind of information shapes pitches, introductions, and the assessments that other firms make when the principal eventually crosses paths with them.
The principal rarely sees this happen. The banker who moved is courteous; the principal continues to bank elsewhere; the new firm makes contact in a way that seems organic. The route by which the contact came is invisible.
What this argues for is awareness of the relationships in play around any given banking arrangement, and a posture toward those relationships that assumes information will travel even where the rules say it should not. The defences are not technical; they are about what the principal does and does not say in the first place.