Supporting increasingly higher rates in wireless networks requires highly accurate clock synchronization across the nodes. Motivated by this need, in this work we consider distributed clock synchronization for half-duplex (HD) TDMA wireless networks. We focus on pulse-coupling (PC)-based synchronization as it is practically advantageous for high-speed networks using low-power nodes. Previous works on PC-based synchronization for TDMA networks assumed full-duplex communications, and focused on correcting the clock phase at each node, without synchronizing clocks' frequencies. However, as in the HD regime corrections are temporally sparse, uncompensated clock frequency differences between the nodes result in large phase drifts between updates. Moreover, as the clocks determine the processing rates at the nodes, leaving the clocks' frequencies unsynchronized results in processing rates mismatch between the nodes, leading to a throughput reduction. Our goal in this work is to synchronize both clock frequency and clock phase across the clocks in HD TDMA networks, via distributed processing. The key challenges are the coupling between frequency correction and phase correction, and the lack of a computationally efficient analytical framework for determining the optimal correction signal at the nodes. We address these challenges via a DNN-aided nested loop structure in which the DNN are used for generating the weights applied to the loop input for computing the correction signal. This loop is operated in a sequential manner which decouples frequency and phase compensations, thereby facilitating synchronization of both parameters. Performance evaluation shows that the proposed scheme significantly improves synchronization accuracy compared to the conventional approaches.