Understanding how stem cells regulate the formation of precise cell-type proportions during organ development is a major developmental-biology goal and will have applications for disease treatment. We previously established that catch-up growth (CUG, accelerated growth after a perturbation period) occurs following impaired long-bone growth, induced by the overexpression of Cdkn1a (p21; a cell-cycle inhibitor) in transient cartilage that drives bone elongation. However, the underlying cellular and molecular mechanisms are mostly unknown. This study aims to identify and characterize the regulation of the stem/progenitor cells responsible for promoting bone growth during normal and perturbed development. To identify the cell population driving CUG, we used genetic mouse models of inducible growth perturbation coupled with lineage tracing, single-cell/nuclei transcriptomics, ex vivo candidate validation, and fluorescence label-retaining assays during both normal and compensatory growth. Bioinformatic analyses, including RNA-velocity and regulon activity, suggested that Gli1+ cells respond to p21-induced injury and drive CUG. Following bioinformatics identification, in vivo and ex vivo validation studies revealed that downregulation of Connective Tissue Growth Factor (CTGF) correlates with Gli1+ cell expansion and identified Pdgfra+ perichondrial cells as a source of Gli1+ cartilage progenitors. Mechanistically, we found that TGF-β1/CTGF axis gain-of-function inhibited both Gli1+ cell expansion and the transition of Pdgfra+ to Gli1+ cells ex vivo, while the loss-of-function models enhanced both. These findings lay the foundation for future investigations into the potential usage of Gli1+ cell populations to serve as fetal progenitors of cartilage stem cells. This could significantly advance our understanding of bone growth and lead to the development of research tools, such as organoids made of cartilage, bone, and perichondrium, and innovative clinical applications, including cellular therapies for genetic disorders.