Way 1
Use the reference function in your parameter file for resources that are already deployed in another template. For that you have to pass the ApiVersion parameter. Refer MsDoc. which follows:
"value": "[reference(resourceId(variables('<AppInsightsResourceGroup>'),'Microsoft.Insights/components', variables('<ApplicationInsightsName>')), '2015-05-01', 'Full').properties.InstrumentationKey]"
You need to change the property that you are referencing from '.InstrumentationKey' to '.properties.InstrumentationKey'.
Refer to Kwill answer for more information.
Way 2
Get the Content of parameter file in PowerShell variable/Object using
$ParameterObject = Get-Content ./ParameterFileName.json
Update the Parameter file values using
#Assign the parameter values using
$ParameterObject.parameters.<KeyName>.value = "your dynamic value"
Pass $parameterObject
to -TemplateParameterObject
parameter
Refer here
Way 3
You have to Add/Modify the parameter file values using (PowerShell/ Dev lang (like Python, c#,...) ). After changing the parameter file try to deploy it.