How to do SQL server native client installation?

No, you don’t need to remove any old native client.

As per Quoting from official document Installing SQL Server Native Client

If a previous version of SQL Server Native Client is also installed on the computer, SQL Server Native Client 11.0 will be installed side-by-side with the earlier version.

Please also note that as per Microsoft after SQL Server 2012 native client download no native clients of future SQL Server versions would be available for download separately and SQL Server 2012 native client can be used for SQL Server 2012 and later versions.

Note that Microsoft will not be releasing a SQL Server 2014 or later version of the SQL Server Native Client. The SQL Server 2012 Native Client (v11, e.g. sqlncli11.dll), can continue to be utilized by SQL Server 2014 and later versions.

Here are the steps to install the Microsoft SQL Server Native client:

• Log on with the appropriate local account to install and launch the Microsoft SQL Server Client.
  
• From the SQL Server Setup media, install the following Shared Features: ...
  
• In SQL Server Configuration Manager, create a new alias in SQL Native Client Configuration (32-bit).