Is it permissible to install a tooth to fill the gap between teeth, in order to improve appearance and avoid the embarrassment resulting from this spacing?

If you have a deformity or an unusual flaw, there is no harm in treating it by installing a tooth. This falls under the category of necessity and is not considered a forbidden alteration of Allah's creation. The rule in cosmetic surgery is: there is no harm in procedures performed out of necessity to remove defects and deformities. The Islamic Fiqh Academy's resolution states the permissibility of essential and necessary cosmetic surgery aimed at restoring the body's organs to their natural form or usual function, or correcting congenital and accidental defects, or removing a disfigurement that causes psychological or physical harm. However, it is impermissible to perform cosmetic enhancement surgery that does not fall under medical treatment and aims to change the natural creation according to whims. Ibn 'Uthaymeen mentioned that if teeth straightening is for increasing beauty, it is forbidden. But if it is to remove a defect, there is no harm in it, citing the Prophet's (peace be upon him) command to the man whose nose was cut off to take a nose of gold.