The balance between the orbital and spin magnetic moments in a magnetic system is the heart of many intriguing phenomena. Here, experimental evidence of a large orbital moment is shown, which competes with its spin counterpart in a ferrimagnetic insulator thulium iron garnet, Tm3Fe5O12. Leveraging element‐specific X‐ray magnetic circular dichroism (XMCD), it is established that the dominant contribution to the orbital moment originates from 4f orbitals of Tm. Besides the large Tm orbital moment, intriguingly, the results also reveal a smaller but evident non‐zero XMCD signal in the O K edge, suggesting additional spin‐orbit coupling and exchange interactions with the nearest neighbor Fe atoms. The unquenched orbital moment is primarily responsible for a significant reduction in g‐factor, typically 2 in transition metals, as determined independently using ferromagnetic resonance spectroscopy. The findings reveal a non‐linear reduction in the g‐factor from 1.7 at 300 K to 1.56 at 200 K in Tm3Fe5O12 thin films. These results provide critical insights into the role of the f orbitals in long‐range magnetic order and stimulate further exploration in orbitronics.