HOW SHOULD I RUN EXE ON ANOTHER LAPTOP WHERE DOSEN;T HAVE SQL SERVER I WANT SAME DATABASE ON THAT LAPTOP WITHOUT INSTALLING SQL SERVER

If you all remotely accessing the original SQL server, that's possible.  If you want to totally get rid of SQL server, unless you have the source code, you will need to have SQL server installed locally.

It also depends on how the application is contacting the SQL server: ODBC, ADO.NET and how the SQL server address is specified: hard-coded or can be modified.

If the SQL server name is hard-coded you can still do SQL Server Alias, but still need an SQL server.

To encrypt data on a laptop, if just by means of OS tool, you can use Windows BitLocker.

Can you install SQL Server on a server on a network on which the other laptop is connected?

Or would SQL Azure (a paid service) would be possible. Because data would be sent/downloaded from the Internet all the time, that would surely introduce latency. Check https://azure.microsoft.com/en-ca/services/sql-database/

If all else fail, you can give a try to LocalDB: https://docs.microsoft.com/en-us/sql/database-engine/configure-windows/sql-server-2016-express-localdb

There are a few network options:

1.) If the laptop is external, VPN to the network where the SQL server is located and connect via address/alias.
2.) If the latop is internal, you can just connect to the instance.
3.) RDP to the laptop and access the application from there.  This would not be a good option if the 2nd laptop is for a different user unless you set up a Remote Desktop server.

If you're hosting the database on the laptop, it would need to always be on or available to connect to the DB.  As suggested, best option would be to move it to a separate box unless you have that laptop sitting somewhere plugged in with power options set to keep it on.