The answer might depend on your DBMS. What type of database is your data in? An enterprise geodatabase, file geodatabase, etc.?
If it is an enterprise geodatabase, I believe you can setup a trigger in the DB that triggers when a new record is inserted into the table that will write that record to the other table.
Unfortunately, I don't think automatically copying records from one table to another upon insert of a new record is something that is possible in a file geodatabase, but someone might be able to correct me if I'm wrong. My best advice for that scenario would be to create a model or script that periodically syncs the original table with the cloned table.
On a side note, I don't know what your use case is for creating the "cloned" table, but if it's just for the purpose of sorting, you can just create a "copy" of the layer in the table of contents in ArcGIS Pro and change the sorting that way. That way you have two different layers in the map with different sorting, but they are both using the same source table so you don't have to deal with two different copies of the same table. Meaning that any updates you make in that table will be reflected in all copies you made in the table of contents.
