This study reports on the fast photon-mediated entanglement of continuously-cooled trapped ions for quantum networking. Two co-trapped barium ions are entangled by collecting single visible photons from each ion using in-vacuo 0.8 NA objectives, interfering them through an integrated fiber-beamsplitter, and detecting them in coincidence. This projects the qubits into an entangled Bell state with a fidelity lower bound of F > 94%. An ytterbium ion is introduced for sympathetic cooling to remove the need for recooling interruptions, achieving a continuous entanglement rate of 250 s⁻¹. Photonic interconnects between quantum processing nodes are essential for large-scale quantum computers. This work demonstrates a high-rate, near-unit fidelity entanglement distribution between computing modules, enabling universal and fully-connected control over a larger Hilbert space. Interconnects between quantum memories also offer opportunities in quantum sensing, communication, and simulation. Trapped ions are attractive for quantum computing and networking due to their natural homogeneity, isolation, and long coherence times. This study achieves a success probability of 2.4(1) × 10⁻⁴ and a fidelity of F ≥ 93.7(1.3)% for photon-mediated entanglement between ¹³⁸Ba⁺ ions. Sympathetic cooling with ¹⁷¹Yb⁺ ions enables an uninterrupted attempt rate of 1 MHz and an ion-ion entanglement rate of 250(8) s⁻¹. The study demonstrates a high-fidelity entanglement rate of 79(3) s⁻¹, with a measured fidelity lower bound of F ≥ 93.7(1.3)%. The results are consistent with the product of the measured ion-photon efficiencies. The extended two-qubit coherence time is 38(13) ms. The study also addresses the challenges of photon collection efficiency, decoherence, and crosstalk, and proposes improvements such as using electro-optic control and Purcell enhancement to increase the entanglement rate. The work highlights the importance of sympathetic cooling in enabling continuous entanglement generation and demonstrates the potential for high-rate remote entanglement between atomic memories. The results are significant for quantum networking and could lead to further advancements in quantum technologies such as scalable ion-trap quantum computers and quantum-limited sensing networks.This study reports on the fast photon-mediated entanglement of continuously-cooled trapped ions for quantum networking. Two co-trapped barium ions are entangled by collecting single visible photons from each ion using in-vacuo 0.8 NA objectives, interfering them through an integrated fiber-beamsplitter, and detecting them in coincidence. This projects the qubits into an entangled Bell state with a fidelity lower bound of F > 94%. An ytterbium ion is introduced for sympathetic cooling to remove the need for recooling interruptions, achieving a continuous entanglement rate of 250 s⁻¹. Photonic interconnects between quantum processing nodes are essential for large-scale quantum computers. This work demonstrates a high-rate, near-unit fidelity entanglement distribution between computing modules, enabling universal and fully-connected control over a larger Hilbert space. Interconnects between quantum memories also offer opportunities in quantum sensing, communication, and simulation. Trapped ions are attractive for quantum computing and networking due to their natural homogeneity, isolation, and long coherence times. This study achieves a success probability of 2.4(1) × 10⁻⁴ and a fidelity of F ≥ 93.7(1.3)% for photon-mediated entanglement between ¹³⁸Ba⁺ ions. Sympathetic cooling with ¹⁷¹Yb⁺ ions enables an uninterrupted attempt rate of 1 MHz and an ion-ion entanglement rate of 250(8) s⁻¹. The study demonstrates a high-fidelity entanglement rate of 79(3) s⁻¹, with a measured fidelity lower bound of F ≥ 93.7(1.3)%. The results are consistent with the product of the measured ion-photon efficiencies. The extended two-qubit coherence time is 38(13) ms. The study also addresses the challenges of photon collection efficiency, decoherence, and crosstalk, and proposes improvements such as using electro-optic control and Purcell enhancement to increase the entanglement rate. The work highlights the importance of sympathetic cooling in enabling continuous entanglement generation and demonstrates the potential for high-rate remote entanglement between atomic memories. The results are significant for quantum networking and could lead to further advancements in quantum technologies such as scalable ion-trap quantum computers and quantum-limited sensing networks.