No, claims to newly found assets should not be made unilaterally, even after the close of a probate case for a specific Will.
In most cases, if an asset of value is found after the close of probate and the court is made aware of the newly found assets, the court will re-open the probate estate and will distribute the newly found asset(s) based on the terms of the Last Will and Testament.
The probate court that settled the Will previously should be notified about the newly found assets.