In general terms, taking thyroid medication can fully replace what the thyroid gland normally does.
It’s important to point out that the thyroid gland doesn't make active thyroid hormones. It makes a precursor that has four iodine molecules on it. Active thyroid hormone has three molecules. The thyroid makes the one with four, your liver takes away one of those iodines to make the three. So you can take the thyroid hormone by mouth, and then the liver does the final step and can regulate much of that process.
TSH is a useful test because that's a measure of what the brain perceives in terms of what the liver's doing, and that can be used by your physician to help judge the dose of oral thyroid medicine as prescribed.
This is something that has to be managed between you and your primary care physician. We can't give you specific advice for that.