How to add an Azure App Service extension via powershell?

You could check this example.

### Install NewRelic Extension for Azure App###write-output "*** Installing New Relic on PROD Site"$WebSite = "your site name"$Kudu = "https://" + $WebSite + ".scm.azurewebsites.net/api/extensionfeed" # Here you can get a list for all Extensions available.$InstallNRURI = "https://" + $WebSite + ".scm.azurewebsites.net/api/siteextensions" # Install API EndPoint$username = "`$UserName"$password = "hxWN9sjrqt9haA3NpG1kTK0QBui2ph7cEGQlcMQhYTiWqDWL9yf1aXGIJHTD"$base64AuthInfo = [Convert]::ToBase64String([Text.Encoding]::ASCII.GetBytes(("{0}:{1}" -f $username,$password)))$invoke = Invoke-RestMethod -Uri $Kudu -Headers @{Authorization=("Basic {0}" -f $base64AuthInfo)} -Method get ###-InFile $filePath -ContentType "multipart/form-data"$id = ($invoke | ? {$_.id -match "NewRelic*"}).id  ### Searching for NewRelic ID Extensiontry {    $InstallNewRelic = Invoke-RestMethod -Uri "$InstallNRURI/$id" -Headers @{Authorization=("Basic {0}" -f $base64AuthInfo)} -Method Put    $Status = ($InstallNewRelic.provisioningState).ToString() + "|" + ($InstallNewRelic.installed_date_time).ToString()  ### Status    Write-Output "NewRelic Installation Status : $Status"    Restart-AzureRmWebApp -ResourceGroupName $ResourceGroupName -Name $WebSite -Verbose ### Restarting the WebApp}catch{$_}