What is the ruling on gradualism in applying Islamic Sharia, with evidence, and are there any controls for it if permissible?

The principle is the obligation to act upon all the rulings of the Sharia (definition). However, if the application of some Sharia rulings leads to a harm that outweighs the benefit of their application, then they are suspended until such a time as they can be applied without an overriding harm. The application of Sharia rulings should be done in the best possible manner, and if their application results in corruption greater than the harm of neglecting them, then they should not be applied. The consideration and estimation of harms falls to the أهل الحل والعقد (those who loose and bind), comprising rulers and scholars.