Should one leave a job as a project manager in a telecommunications company that provides services to institutions, some of which are haram, such as banks and insurance companies, and should this ترك (leaving) be immediate or gradual?

There is no objection to your work if it is limited to providing service to companies, universities, airports, and the like, for which it is highly probable that they use the internet for permissible purposes. It is not permissible to provide the service to usurious banks or commercial insurance companies, as this entails assisting them in their prohibited work. Allah Almighty says: (And cooperate in righteousness and piety, but do not cooperate in sin and aggression. And fear Allah; indeed, Allah is severe in penalty) Al-Ma'idah/2. If the company performs both permissible and prohibited activities, and your work is limited to the permissible, then there is no objection to you remaining in this job. However, you are not permitted to act on behalf of another in their prohibited work.