Cognitive radio (CR) has been considered as a promising technology to enhance spectrum efficiency via opportunistic transmission at link level. Basic CR features allow secondary users (SUs) to transmit only when the licensed channel is not occupied by primary users (PUs). However, waiting for an idle time slot may lead to large packet delays and high energy consumption. We further consider that the SU may decide, at any moment, to use another dedicated way of communication (4G) in order to transmit his packets. Thus, we consider an Opportunistic Spectrum Access (OSA) mechanism that takes into account packet delay and energy consumption. We formulate the OSA problem as a Partially Observable Markov Decision Process (POMDP) by explicitly considering the energy consumption as well as packets’ delay, which are often ignored in existing OSA solutions. Specifically, we consider a POMDP with an average reward criterion. We derive structural properties of the value function and we show the existence of optimal strategies in the class of the threshold strategies. For implementation purposes, we propose online learning mechanisms that estimate the PU activity and determine the appropriate threshold strategy on the fly. In particular, numerical illustrations validate our theoretical findings.