. . . . . . . . plant hormone promotes the mechanism of apical dominance in plants.

Auxin is the plant hormone that promotes the mechanism of apical dominance in plants. It promotes apical dominance by suppressing the activity of lateral buds.
Auxins are a group of naturally occurring and artificially synthesized plant hormones and play an important role in the regulation of plant growth. Auxin means ‘to enlarge’ and enhances cell division, elongation and differentiation, embryonic development, apical dominance and transition to flowering.