Yes. A high TSH level suggests hypothyroidism, which is definitely linked to high blood pressure. The exact reason for this association is unclear, but it is related to altered neural control of blood vessels and to chemicals like norepinephrine, prolactin, and TSH. Hormone replacement therapy is the treatment for hypothyroidism and should typically reduce TSH and normalize blood pressure. Once your thyroid problem is under control you can have your blood pressure checked to see if remains elevated and needs treatment, or if it just goes back to normal.