How to make a sauce based on tea

Interesting question. My first thought would be to try just poaching the fish in the tea. That should transfer more of the flavour than, say, steaming it. Google finds this recipe where they use an unnamed green tea.

You could brew a very strong batch of the tea, and reduce that to the desired level. You can use that as a base for a sauce to accompany the fish.

Tea leaves are excellent for smoking. I have had green tea smoked duck, gorgeous. Earl Grey works beautifully in desserts.

Good pu-erh tea is now often paired with chocolate, so a ganache might work nicely; simmer some cream with the tea leaves, strain into bittersweet chocolate while the cream is still near boiling, stir aggressively until smooth. A pu-erh and chocolate custard would likely work fairly nicely, or something along the lines of

Marbled tea eggs would probably also work well; this involves simmering pu-erh tea, soy sauce, sugar, and water together, often with star anise; cracking gently hard-boiled eggs all over, without breaking the shells off. Soak overnight in the solution and you should get a pretty nice aromatic and pre-seasoned boiled egg.

I suspect that pu-erh brewed with orange peels, then integrated into minced shallots cooked with butter, would work nicely together, though I'm not sure what the best candidate for the sauce would be; perhaps roasted pork or maybe some boiled udon.