Is it possible to Azure DevOps to retrieve my project from private repository?

I would like to use Azure DevOps, but my company's code is on a private server. Actually, it resides on a Subversion server in a private IP.

There is a way to use Azure DevOps to retrieve my code or build straight from my on-premise server?

The answer is Yes. You can integrate your on-premises Subversion server with Azure Pipelines.

If your server is reachable from the hosted agents, then you can use the hosted agents to run manual, scheduled, or CI builds.

Otherwise, you must set up self-hosted agents that can access your on-premises server and fetch the code.

Check here for more information.

Since your private repository resides on a Subversion server in a private IP. You need to build a self-hosted agent on the on-premise server machine or on a machine which can access to the Subversion server.

When you start to create a azure pipeline(Azure devops Project portal-->Pipelines-->New Pipeline), You can follow the wizard to choose the Subversion as Where is your code and Click the Add connection to create a subversion service connection. Refer to this tutorial to create a azure pipeline.

After the pipeline is created. Select your private agent pool where your self-hosted agent resides. So that when you run the pipeline, it will run on your self-hosted agent which is hosted on your on premise machine. Since your Subversion server is accessible on your on premise machine, the pipeline will be able to retrieve your code and build on our self-hosted agent. See below screenshot.