Conditional MS SQL replication
Reference:


Transactional Articles - Specify How Changes Are Propagated
sp_addarticle (Transact-SQL)
Transactional Replication insert only new Records


Yes it is possible with transactional replication.  I am assuming initially you want all data to be replicated to secondary. For that you will do a reinitialize and snapshot. From there on if your article is set up I mentioned below only new inserts will be replicated. For update you can do the same if you chose to.

When using sp_addarticle set @del_cmd  value to NONE.

If you do it from GUI it will look something like this.