In Azure DevOps, we could run pipeline to actualize the pull requests in the CI process. There is still Release which will run pipeline in the CD process. Could we use the pipeline to do the CD instead of using Release? Could anyone tell me why would we need to use release?
Classic pipelines are created in the Azure DevOps web portal with the Classic user interface editor. There is a clear separation between the building and deployment processes - for example, you can define a pipeline to build, test your code, and finally publish your artifact (binary) and then you can define a release pipeline to consume your binary (artifact) and deploy it to specific targets.
This separation (build vs release) no longer exists when using YAML pipelines - you can use a single YAML pipeline to both build and deploy your application, if you wish so.
So, in your particular scenario, and in case you're not doing it already, I'd recommend to create a YAML pipeline with all the steps you need to run as part of the pull request.