SQL native client installation App team had suggested to reinstall SQL native client for SQL server 2012.
My question here is can I download the SQL server native client installation file and just install over the existing native client?
Or do I need to remove the existing native client and install again?
do I need to remove the existing native client and install again?

No you do not need to remove any old native client. 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.