If the eyebrow hair is secondary to shaving or trimming frequently it will not come back. There have been reports that Latisse can stimulate hair growth and the only other option is an eyebrow transplant.
First, a thorough examination and blood tests to make sure that there is no underlying systemic problem like thyroid issues. If everything comes back normal, I inject some patients with intralesional cortisone. This generally gives a prompt response. Other options are topical minoxidil or topical Rogaine. It may take several months of application to see a change.