To meet the bold requirements of future generation networks, emerging technologies such as opportunistic spectrum access, multi-tier networks, full-duplexing and cooperative networks have to be exploited. In this paper, we propose to blend all the above and globally optimize a relay-aided cognitive radio network composed of a licensed link and an opportunistic link, which is helped by a full-duplex relay node. The opportunistic transmission is allowed provided that a minimum Quality of Service (QoS) constraint is met at the licensed user. First, we derive the achievable rate region under two relaying schemes, namely Decode-and-Forward (DF) and Compress-and-Forward (CF). Then we investigate the optimal power allocation policies for the opportunistic user and the relay under an overall power constraint. The resulting optimization problems are non-convex programs because of the non-trivial operations at the relay (for both CF and DF) and, for DF relaying, the non-convex QoS constraint. Remarkably, the optimal solution is stated in closed-form for CF, whereas it is obtained numerically for DF. Finally, we evaluate numerically the network performance under the two relaying schemes. It turns out that DF outperforms CF only when the relay is close to the opportunistic transmitter and that CF relaying is always useful. © 2021 IEEE.