I’m looking for a simple integration that will allow me to post timesheets directly from devops, and create tasks for work items in Freeagent if needed.
It should be possible to implement without any externally hosted services. DevOps plugins allow for basic data storage and calling remote APIs.
If it doesn’t exist I’ll probably make it.
Hi there 
Jamie from FreeAgent here, thanks for reaching out. There does look to be a few integrations for FreeAgent and Azure Devops, you should be able to determine from their docs whether they suit your needs to be able to post timesheets and create tasks.
There is one integration built and maintained by Integrately: How to integrate FreeAgent & Azure DevOps | 1 click ▶️ integration
As well as another built and maintained by Tray io: https://tray.io/connectors/azure-dev-ops-freeagent-integrations
If none of these are sufficient, then you likely will have to make it as you say. I hope this helps! 
Best regards,
Jamie