I have a high tsh after thyroidectomy 4 years ago. if left untreated, what might occur?

An elevated TSH the vast majority of the time is caused by hypothyroidism, which is an underactive thyroid. Untreated under active thyroid can lead to serious consequences including congestive heart failure depression fatigue and death.

How high? If it is greater than 5 you are hypothyroid. For information on this topic: https://www.niddk.nih.gov/health-information/endocrine-diseases/hypothyroidism#:~:text=Hypothyroidism%2C%20also%20called%20underactive%20thyroid,the%20front%20of%20your%20neck.