I finished Ph.D several months ago and planning to apply for postdoc positions. I am preparing my research statement. I would like to ask some experts to review it before uploading that. Is it ethical to ask my Ph.D advisor to study and review it? I do not know how and to whom can I send my research statement to check and review that before uploading for postdoc position.
Yes, your PhD advisor should definitely go over your research statement. Getting you a job is part of his or her job.
The people writing your recommendation letters should also go over your research statement and give you feedback. It will also help them write letters.