In order to enable SharePoint Online PowerShell Script execution from your remote machine, below are the steps required to follow on remote machine,

Step 1

SharePoint Server 2013 Client Components SDK – Download and Install at your Remote machine, Download SharePoint Server Client SDK .
This is required to enable usage of CSOM to your PowerShell script for O365 tenant.
Download as per available remote machine environment,

Install after download,

Step 2

Install Windows PowerShell 3.0 from Windows Management Framework 3.0 .

Step 3

Install the SharePoint Online Management Shell from the Microsoft Download Center .

Step 4

Set the policies, if not already set,

Check policies by using Windows PowerShell script command,

Get-ExecutionPolicy -List

The result will look similar to the following sample output:

Scope    ExecutionPolicy
—–    —————
MachinePolicy          Undefined
UserPolicy          Undefined
Process          Undefined
CurrentUser       RemoteSigned
LocalMachine          AllSigned

If not as above, use below command,

Set-ExecutionPolicy -ExecutionPolicy <PolicyName>

e.g to set CurrentUser policy,

Set-ExecutionPolicy -ExecutionPolicy  CurrentUser

When it ask for value use below,
Click here for detailed information on RemoteSigned
Hope you find this article useful.