The device has an infusion cannula (11) and/or a puncture point for piercing into a body of a patient. A housing is provided with a contact area (2) for fitting of the device on an application point at the body of the patient during application of an insertion head (12). A housing part (1a) is moved into a basic position after insertion of the insertion head into a retaining unit. The retaining unit separates the insertion head to start an insertion movement such that the device performs a larger part of the insertion movement lost by the retaining unit. Independent claims are also included for the following: (1) an arrangement comprising an insertion device (2) a method for applying an insertion head.