I have a Looker ( Google cloud core instance) , does looker action hub will not work in this instance and can we add custom action here?
The action hub should be available to you if you have a Public IP setup for your Looker Core instance. If it is a Private IP setup, then it will not work out of the box.
According to this documentation, the Action Hub is disabled by default on Looker Core instances and needs to be enabled in the Admin panel - perhaps this is why you are not seeing it as available right now?