My tarragon plant has gone nuts and I need ideas for using it.
Most fresh herbs can be used to make infusions to use when the herbs are out of season. You can infuse oil, vinegar, simple syrup or vodka depending on what sort of dishes you typically cook.
You can also make herb sauces (take inspiration from a chimichurri or pesto, but substitute for the herbs you have on hand) or herb butters (mix chopped herbs with softened butter, shape into a log, then chill or freeze).
As Joe points out, if you have more than you can use in recipes right now, there are various ways to preserve it for later use. Here's a link that gives some detailed instructions (including for some of Joe's suggestions, and some others).
In particular, I would also note the freezing option if you don't want to leave your options open for future use. Many fresh herbs can be chopped and put into ice cube trays with a little water to create "herbed flavor cubes" which can be added to whatever dishes you want later on. Herbs with a lot of moisture like tarragon generally lose a lot of flavor when dried, and simply freezing tarragon without putting it in something may also drive a lot of the flavorful moisture out. (Some people find that blanching very briefly before cooling and freezing tends to retain the fresh flavors better, though I've had mixed experience with this. It may retain color better though.)