TestComplete integration with TestRail

There is not a direct integration from TestComplete to TestRail but TestRail has a REST based API that you can easily send test cases to TestRail and collect test results.

Also both products integrate with JIRA which can be an intermediary

Please take a look at the REST API section on this page

https://www.gurock.com/testrail/tour/testing-integration

Cheers

Lino