Al-jawab billahi at-taufeeq (the answer with Allah's guidance)
Your father-in-law is a Mahram. Therefore, you will not have to adopt the Hijab in front of him.
Allah Ta'ala says,
"And say to the believing women, that they lower their gaze cast down their eyes and guard their chastity, and do not reveal their adornment except that which is outward (face and hands); and let them draw their veils over their neck, and not reveal their adornment except to their husbands, or their fathers, or their husbands' fathers, or their sons, or their husbands' sons, or their brothers, or their brothers' sons, or their sisters' sons, or their women, or what their right hands own, or such male attendants having no sexual desire, or children who have not yet attained knowledge of women's private parts; nor let them stamp their feet, so that their hidden ornament is known. And, O believers turn to Allah all together, in order that you prosper." (24:31)
However, it should be remembered that if there is a fear of temptation (Fitna), then it would be necessary for you to wear the Hijab in front of him as well.
