This study explores the use of discrete time crystals (DTCs) as a resource for quantum-enhanced sensing. DTCs are a special phase of matter where time translational symmetry is broken through periodic driving. The authors propose and characterize a mechanism to generate a stable DTC in a disorder-free many-body system with indefinite persistent oscillations, even in finite-size systems. They demonstrate that this system can measure spin exchange coupling with strong quantum-enhanced sensitivity. As the spin exchange coupling varies, the system undergoes a sharp phase transition into a non-DTC phase, where the performance of the probe decreases. This phase transition is characterized as second-order and its critical properties are determined through finite-size scaling analysis. The probe's performance is independent of the initial state and may even benefit from imperfections in the driving pulse. The study also explores the sensing capability of the DTC system. It shows that the DTC phase provides extreme sensitivity to the exchange coupling across the entire DTC phase, achieving quantum-enhanced sensitivity. The probe's performance is independent of the initial state, and the precision enhances by increasing imperfection in the pulse to a certain value. The non-DTC phase is characterized by ergodic behavior in the thermodynamic limit. The authors use quantum parameter estimation theory to analyze the system's ability to infer an unknown parameter in a Hamiltonian by observing the evolution of the probe's state. They show that the quantum Fisher information (QFI) is a measure of the precision of parameter estimation, and that the DTC system can achieve higher precision than classical sensors. The QFI scales with the system size, and the DTC system can achieve a higher QFI than classical sensors. The study also explores the effect of imperfections on the DTC system. It shows that the DTC system is robust against uniform imperfections in the driving pulse. However, non-uniform imperfections can affect the system's performance. The study also shows that increasing imperfection in the pulse can enhance the precision of the DTC system. The authors conclude that the DTC system is an excellent resource for quantum-enhanced sensing. It provides high precision in measuring coupling strength and is robust against imperfections in the driving pulse. The study also shows that the DTC system undergoes a second-order phase transition, which can be used as a resource for quantum sensing. The results demonstrate that the DTC system is a promising candidate for quantum-enhanced sensing applications.This study explores the use of discrete time crystals (DTCs) as a resource for quantum-enhanced sensing. DTCs are a special phase of matter where time translational symmetry is broken through periodic driving. The authors propose and characterize a mechanism to generate a stable DTC in a disorder-free many-body system with indefinite persistent oscillations, even in finite-size systems. They demonstrate that this system can measure spin exchange coupling with strong quantum-enhanced sensitivity. As the spin exchange coupling varies, the system undergoes a sharp phase transition into a non-DTC phase, where the performance of the probe decreases. This phase transition is characterized as second-order and its critical properties are determined through finite-size scaling analysis. The probe's performance is independent of the initial state and may even benefit from imperfections in the driving pulse. The study also explores the sensing capability of the DTC system. It shows that the DTC phase provides extreme sensitivity to the exchange coupling across the entire DTC phase, achieving quantum-enhanced sensitivity. The probe's performance is independent of the initial state, and the precision enhances by increasing imperfection in the pulse to a certain value. The non-DTC phase is characterized by ergodic behavior in the thermodynamic limit. The authors use quantum parameter estimation theory to analyze the system's ability to infer an unknown parameter in a Hamiltonian by observing the evolution of the probe's state. They show that the quantum Fisher information (QFI) is a measure of the precision of parameter estimation, and that the DTC system can achieve higher precision than classical sensors. The QFI scales with the system size, and the DTC system can achieve a higher QFI than classical sensors. The study also explores the effect of imperfections on the DTC system. It shows that the DTC system is robust against uniform imperfections in the driving pulse. However, non-uniform imperfections can affect the system's performance. The study also shows that increasing imperfection in the pulse can enhance the precision of the DTC system. The authors conclude that the DTC system is an excellent resource for quantum-enhanced sensing. It provides high precision in measuring coupling strength and is robust against imperfections in the driving pulse. The study also shows that the DTC system undergoes a second-order phase transition, which can be used as a resource for quantum sensing. The results demonstrate that the DTC system is a promising candidate for quantum-enhanced sensing applications.