Can you execute/run Terragrunt repositories from Terraform Cloud UI and if not what is the best approach toa run Terragrunt repo in the cloud?
Terragrunt is third-party software that wraps Terraform CLI and runs it for you.
Terraform Cloud is also, at its core, software that wraps Terraform CLI and runs it for you. You can use either Terragrunt or Terraform Cloud to run Terraform CLI, but not both.
An exception to this situation is that Terraform CLI can optionally be configured to act only as a client to the Terraform Cloud API rather than performing actions directly itself. This facility is called “Remote Operations” and when activated it allows a situation where you can run Terraform CLI to ask Terraform Cloud to run Terraform CLI remotely.
Since Terragrunt is also a wrapper that runs Terraform CLI, you can choose to use Terragrunt to run Terraform CLI when configured for remote operations, in which case Terragrunt will indirectly trigger Terraform Cloud-managed remote execution of Terraform CLI.
The opposite arrangement is not possible. Terraform Cloud exclusively runs Terraform CLI, which means there’s no place to introduce another Terraform CLI wrapper such as Terragrunt into the system unless Terragrunt is the top-level wrapper, run directly by you.