What should I do regarding renewing the internet contract for one of my irreligious relatives, given my fear that he might use the internet for illicit purposes, and he might become angry if his need is not met or if I do not contact him?

The basic principle is that a Muslim should benefit his brother and help him with everything that benefits him in his religion and his worldly life, to the best of his ability.

A relative's request to connect the internet to his home for watching television is a permissible service. The mere possibility of him using it for forbidden things does not prevent providing the service, and the sin is on him, not on you; because you did not directly assist him in the forbidden act, nor did you intend that.

Assisting in sin and aggression is of four types: 1. Direct and intentional: Like giving alcohol with the intention of helping someone drink it. (Forbidden) 2. Direct and unintentional: Like selling forbidden items that have no permissible use, without intending to assist in the forbidden act. (Forbidden) 3. Indirect and intentional: Like giving money to buy alcohol. (Forbidden) 4. Indirect and unintentional: Like selling something that can be used for both permissible and forbidden purposes without intending to assist in the forbidden act, or giving money without intending to assist in a forbidden act. If it is then used for a forbidden purpose, there is no sin on the giver. (Permissible)