Temporal knowledge graphs (TKGs) with evolving event representations serve as critical infrastructure for AI applications like information retrieval and rumor detection. Current TKG completion methods face three key limitations: (1) Conversion of quadruple structures to triplets constrains temporal information representation, (2) Cross-space interactions among entities, relations, and timestamps are challenging, and (3) Neighborhood contexts are underutilized and disambiguation mechanisms for polysemic elements are absent. To address these challenges, we propose the Quadruple-based Neural Discourse-Aware (Q-NDA) network. Our framework employs space-specific encoders for entity, relation, and timestamp representations, coupled with an Information Discourse Module enabling bidirectional cross-space communication. The architecture incorporates contextual disambiguation and neighborhood attention mechanisms to resolve semantic ambiguity while aggregating structural patterns from adjacent quadruples. This constitutes the first systematic approach addressing completion in TKGs through integrated neighborhood exploitation. Evaluations on benchmark datasets demonstrate Q-NDA’s superior performance, particularly achieving state-of-the-art results on the geometrically complex GDELT dataset - yielding 19.3% average metric improvement and 20.5% MRR gain over existing methods.