You can use rest api to trigger the tests when other CD-pipelines run.
If you want to run the tests in a separate CI pipeline. You need to create a CI pipeline to run the tests for this test repository. Then add a script task in the CD pipeline to call build queue restful api. Please check below script example in powershell task.
$url = "$(System.TeamFoundationCollectionUri)$(System.TeamProject)/_apis/build/builds?api-version=5.1"
$qbody = '{
"definition": {
"id": "the definition id of the test CI pipeline"
}
}'
$update = Invoke-RestMethod -Uri $url -Headers @{Authorization = "Bearer $env:SYSTEM_ACCESSTOKEN"} -ContentType "application/json" -Method post -Body $qbody
You aslo need to go to the agent job and check Allow scripts to access the OAuth token.

Another way to trigger the test CI pipeline from CD pipeline is to add Trigger Azure DevOps Pipeline task in CD pipeline and configure it to trigger the test CI pipeline.