Can anyone advise on how to build an application using TeeChart on hosted build agents in Azure DevOps? As far as I understand it is not possible to install something on the build agent so it is not possible to install the license prior to the build.
No, you can not compile TeeChart applications on Hosted VSTS agents.
For VSTS Hosted agents, TeeChart is not installed, and there is no way to install additional software on Hosted agents.
The workaround is using private agent where you have the IDE installed for VSTS build. More details about deploying a private agent, you can refer the document.