This paper investigates a pinching-antenna (PA)-enabled cognitive radio network, where both the primary transmitter (PT) and secondary transmitter (ST) are equipped with a single waveguide and multiple PAs to facilitate simultaneous spectrum sharing. Under a general Ricean fading channel model, a closed-form analytical expression for the average spectral efficiency (SE) achieved by PAs is first derived. Based on this, a sum-SE maximization problem is formulated to jointly optimize the primary and secondary pinching beamforming, subject to system constraints on the transmission power budgets, minimum antenna separation requirements, and feasible PA deployment regions. To address this non-convex problem, a three-stage optimization algorithm is developed to sequentially optimize both the PT and ST pinching beamforming, and the ST power control. For the PT and ST pinching beamforming optimization, the coarse positions of PA are first determined at the waveguide-level. Then, wavelength-level refinements achieve constructive signal combination at the intended user and destructive superposition at the unintended user. For the ST power control, a closed-form solution is derived. Simulation results demonstrate that i) PAs can achieve significant SE improvements over conventional fixed-position antennas; ii) the proposed pinching beamforming design achieves effective interference suppression and superior performance for both even and odd numbers of PAs; and iii) the developed three-stage optimization algorithm enables nearly orthogonal transmission between the primary and secondary networks.