Transactional Replication Update process
If you need your combined table updated automatically you would need to put triggers on the 9 tables which have been replicated to your server.

A better option would be to put an indexed view on top of the 9 tables (I'm assuming that your table is created with a single query).  This way there's no need to handle updating your table as the indexed view would always be up to date and you can simply just query it.  As it is an indexed view you can add any non-clustered indexes to it as needed to make performance nice and fast.

If the query to combine the 9 tables together into your schema a normal view should be fine.  Just have your report query the view, and the data will always be up to date.  The big difference between a normal view and an indexed view (above) is that with a normal view the indexes go on the 9 replicated tables where with an indexed view the indexes can be placed on the view directly.

What it comes down to, is that there isn't any need for an additional table.