Rinse the wild rice under cold water in a fine-mesh sieve and leave to drain.
Heat the olive oil or unsalted butter in a medium saucepan or lidded casserole dish on a medium heat.
Add the chopped onion, celery and carrot and fry, stirring occasionally, until the vegetables have softened and the onion is translucent, about 5 to 7 minutes.
Stir in the drained wild rice and dried thyme and toast for 2 minutes, stirring constantly.
Pour in the stock, season with salt and black pepper, and stir to combine.
Bring to the boil over a medium-high heat, then reduce to a low heat, cover and simmer without lifting the lid for 45 to 50 minutes, or until the rice is tender and most of the liquid has been absorbed.
Remove from the heat and leave, covered, for 10 minutes to steam and become fluffy.
Uncover, fluff the rice with a fork, taste and adjust the seasoning if necessary, then serve warm.