I have been diagnosed with primary hyperparathyroidism, can I just wait to see what happens?

No.  There is uniform agreement in the medical profession that persons with diagnosed primary hyperparathyroidism require surgery for removal of the abnormal parathyroid adenoma.  You may not be experiencing any of the common signs or symptoms such as bone pain, kidney stones, or abdominal discomfort; nevertheless, the constantly elevated parathyroid hormone level is causing thinning of your bones and abnormally elevated calcium.  Ultimately this leads to osteoporosis which may result in bone fractures in later years of life.  The "wait" strategy is no longer considered a reasonable option for most people.