Motivated by recent deep mutational scanning (DMS) experiments, we have carried out a diverse set of computations to better understand the distribution and contributions of allostery hotspot residues in a transcription factor, TetR. These include extensive atomistic simulations and free energy computations for different functional states of TetR, machine learning analysis of the DMS data and a statistical thermodynamic model for the experimental induction data for the WT protein and a handful of hotspot mutants. Collectively, these computations provided insights into the structural and energetic basis of allostery in TetR, and the distinct contributions of allostery hotspots. The results highlight that the allostery function (i.e., the induction activity) of TetR can be modulated by perturbing both inter-domain coupling and intra-domain properties, such as the population of the binding-competent conformation of each domain. This mechanistic degeneracy qualitatively explains the broad distribution of allostery hotspots across the protein structure observed in the DMS experiments, and also informs the design of strategies aimed at identifying allostery hotspots. The mechanistic framework and the multi-faceted computational approaches are expected to be applicable to the analysis of other allostery systems, especially those sharing the similar two-domain structural topology, and to the design of allostery modulators.