You cannot use Dataclips with Heroku Postgres instances running Shield plans.
Shield database instances are designed specifically to only allow connections from your applications running in your Shield Private Space. That is why you cannot connect to them with Dataclips.
The one exception is the Mutual TLS (mtls) feature of Heroku Postgres. Dataclips does not support this, but you may be able to find another vendor that provides similar functionality and offers mtls support:
Just to clarify, you can use Dataclips for Private Heroku Postgres instances that are hosted in Private Spaces. Private-tier databases in Private Spaces also have additional protections compared to those in the Common Runtime. This article has a good overview of the features and differences between Private and Shield databases:
If you choose to use a Shield instance you also have the option of create an app inside your Space to provide Dataclips-like functionality. Unfortunately we don't have an official recommendation for what tool could do that. We recommend reviewing the Postgres wiki client list and seeing which options meet your needs and that you could install inside a Space: