Keeping data in old Database (SQL 2008) identical to new Database (SQL 2016)?
Converted from comments:


  According to Replication Backward Compatibility, Transactional Replication will not work between a 2016 Publisher and a 2008 Subscriber, but Merge Replication would be supported. Check out Merge Replication to see if that will suit your needs. – Scott Hodgin 
  
  Or Upgrade to 2014 and it will be backward compatible to 2008 for transactional replication. Once You have a steady ship, you can move ahead to later versions if needed. – Ramakant Dadhichi