This paper presents a conservative infrared extension of General Relativity where late-time cosmic acceleration emerges from a curvature-regulated modification of gravitational time dilation. The proposed framework introduces no additional propagating degrees of freedom and remains fully covariant at the action level. Key highlights of the research: * Mechanism: Uses an exponential suppression factor to ensure exact GR recovery in high-curvature environments (solar system/galactic scales) while activating modifications only at cosmological scales. * Cosmological Impact: The model reproduces $\Lambda$CDM behavior at late times and addresses the Hubble tension ($H_0$) without invoking dark energy or fine-tuned vacuum energy. * Falsifiability: Predicts a cumulative proper-time drift in ultra-low curvature environments, providing a direct path for experimental testing via future deep-space atomic clock missions. * Mathematical Consistency: Provides a detailed formulation including field equations and background evolution analysis.