Can I add new tables to a transactional replication subscriber I'm looking into using transactional replication in MS SQL Server 2016 to create a reporting database from our production HR system.

I'm wondering if it's possible to create new stored procedures and tables on the reporting database which will not be dropped as part of the replication sync?
if it's possible to create new stored procedures and tables on the
  reporting database which will not be dropped as part of the
  replication sync?


Yes, you can create new stored procedures and tables on the reporting database.

When creating a publication, you choose the tables and other database objects that you want to publish. Objects that are included in the publications get replicated. You are free to add other objects in the subscriber database.

Read this document which details about publication and limitations: 
Publish Data and Database Objects