Moving Pickpocket is a set of two purchasable power-ups, one for Sly Cooper and the other for Bentley, in Sly Cooper: Thieves in Time. It costs 500 coins and is available after completing "Shopping Spree" for Sly and "Up in Smoke" for Bentley.
This power-up allows the user to move while pickpocketing (press while behind a guard with coins and/or loot). This can allow the user to keep up with a moving guard so that a pickpocket attempt has less of a chance to whiff. However, moving while pickpocketing comes with a risk: you can touch the guard, and therefore alert him/her to your presence, before or even after you've finished the pull. This is especially possible when a moving guard suddenly stops moving to take break for a few seconds.