The thermodynamic uncertainty relation sets the minimal bound of the cost-precision trade-off relation for dissipative processes. Examining the dynamics of an internally coupled system that is driven by a constant ther- modynamic force, we however find that the trade-off relation of a sub-system is not constrained by the minimal bound of conventional uncertainty relation. We made our point explicit by using an exactly solvable model of in- teracting oscillators. As the number (N ) of interacting oscillators increases, the uncertainty bound of individual oscillators is reduced to 2kB T /N upon full synchronization under strong coupling. The cost-precision trade-off for the sub-system is particularly relevant for sub-cellular processes where collective dynamics emerges from multiple energy-expending components interacting with each other.