No, the first transfer of ownership of an artwork, whether acquired through gift or inheritance, does not trigger a resale royalty obligation. The Artist Resale Royalty Scheme specifically applies to “resales,” which are any subsequent transfers of ownership following the artwork’s first transfer.
As a “Resale” does not include the first transfer of ownership of the artwork (irrespective of whether the first transfer of ownership was made for money or other consideration) you would not need to pay a resale royalty.
However, if you decide to then sell an artwork that was gifted to you or inherited by you, and the criteria for a qualifying resale is met, then a royalty will be due.
You can check if there has been a qualifying resale on our flowchart here: Is there a “qualifying resale”?: