Linking clients and projects across boards

I’m still new and learning at the moment with this, so please forgive me if this is elementary, but -

I have a board for projects, and a board for clients. I’d like to be able to add a project to the project board and select a client from the clients column (which is linked to the clients board). I’d then like for the project to appear listed as a subitem beneath the client on the client board.

So, something like this:

And as soon as I select a client from the list, this is what I’d like to have happen (here I have just put it in manually):

How do I handle this? It seems like I’d need some way of finding the correct row in the client board that matches the client that has been chosen and add a sub-item with correctly mirrored information from the project board, but I don’t see a clear path to that through the automations or linking options.