A royalty is payable on each resale.
Who is liable in each instance is answered by section 17 of the Act. The seller is always liable, and generally their agent will be jointly and severally liable. Generally a buyer won’t be liable unless no agent is involved.
To give two contrasting examples:
Where a gallery buys from an auction house or art consultant (who is acting behalf of a seller), the liable parties will be the seller and the seller’s agent (i.e. auction house or art consultant). It’s unlikely the purchasing gallery would be liable in this scenario (unless the seller actually has no agent, and the buyer has no agent).
Where a gallery buys directly from another gallery (without using any agents), then the buying gallery will indeed be jointly liable with the selling gallery to pay the royalty on the purchase. (How the two galleries share this liability will be a private matter). The buying gallery will then be liable as a seller if/when they come to resell.