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This paper analyses the joint relay selection and pre-coder designing problem for underlay cognitive relay networks (CRNs) where each node is equipped with multiple antennas. We first design the energy-efficient precoders for relay nodes and then perform the relay selection based on the maximum achieved energy efficiency (EE). Precoders are derived for relay nodes to satisfy the transmit power constraint at relay nodes and interference constraint at the primary receiver (PR). Based on the optimal precoders, we analyse the impact of relay selection on the EE of the secondary system (SS). Closed-form expressions for relay precoders are obtained using the combination of fractional programming theory, singular value decomposition (SVD), and Lagrangian multiplier method. Simulation results validate the impact of joint relay selection and precoder designing on the achievable EE.