This paper presents the control framework that has been proposed and successfully employed within the TRIDENT EU FP7 project, the aim of which is to develop a multipurpose Intervention Autonomous Underwater Vehicle (I-AUV) exhibiting smart manipulation capabilities, for interventions within unstructured underwater environments. In particular, the work focuses on the exploitation of the highly redundant system for achieving a dexterous object grasping, while also satisfying a set of conditions of scalar inequality type to be achieved ultimately. These represent safety and/or operational-enabling conditions for the overall system itself, such as, for instance, respecting joint limits and keeping the object grossly centered in the camera system. Thus the design of a control architecture exhibiting such a property first required an extension of the classical task priority framework, to be performed in such a way as to also account, in a uniform manner, for inequality conditions to be achieved ultimately. Then, following a description on how such an extension has been made, both simulations and experimental trials are successively presented to show how the developed TRIDENT I-AUV system is able to properly exploit all the redundant degrees of freedom for achieving all the established objectives.