  Coherence of a quantum state intrinsically depends on the choice of the
reference basis. A natural question to ask is the following: if we use two or
more incompatible reference bases, can~there be some trade-off relation between
the coherence measures in different reference bases? We show that the quantum
coherence of a state as quantified by the relative entropy of coherence in two
or more noncommuting reference bases respects uncertainty like relations for a
given state of single and bipartite quantum systems. In the case of bipartite
systems, we find that the presence of entanglement may tighten the above
relation. Further, we find an upper bound on the sum of the relative entropies
of coherence of bipartite quantum states in two noncommuting reference bases.
Moreover, we provide an upper bound on the absolute value of the difference of
the relative entropies of coherence calculated with respect to two incompatible
bases.
