When is At-Tayammum prescribed?

1. During the scarcity of water or its unavailability

Allah, The Most Exalted, says: “... and you find no water, perform At-Tayamum.” (Al-Ma’idah:6) But it’s said that a person is not considered as having a lack of water when he has not searched for it.
2. When one is incapable of using water, even when it is available

For example, a sick and/or an eldery person who cannot move and has no one to help him/her perform wudu’.

3. When one fears he will be harmed by using water

Examples include:
a- A sick person whose use of water (for pruificaton) may aggravate his sickness;
b- A person experiencing extreme cold and does not have the means to warm water, coupled with a strong fear that he may fall sick from the use of cold water.
This is because the Prophet ﷺ approved of the action of Amr Ibn Al-‘As when he led his people in prayer and he had performed at-tayammum due to the extreme cold.[ narrated by Abu Dawud.]
c-Someone far away from others or on a long journey with no water except a little for him to drink and he is not able to get other water.
source: https://www.al-feqh.com/en/tayammum-dry-ablution