What should one do if someone threatens to expose and "disgrace" their immoral past should they not abandon their call to God, after they have repented and desired to change their life?

You have committed a great error by succumbing to the whisperings of Satan, especially since you are among the people of knowledge and da'wah (preaching), which makes the error even greater. Nevertheless, the door of repentance is open, so repent to your Lord with sincere repentance and regret what emanated from you. As for the man's threat, do not surrender to him and continue your da'wah. Try to advise him and clarify to him that what happened was a slip and you have repented from it. If advice does not work, use allusions (al-ma'arid) to deny the accusation. If your disgrace will tarnish the image of religious people, you can engage in da'wah through other means or in places where this person will not become aware of it, while continuing to advise him and clarify that Allah accepts repentance.