  Sequential sharing of nonlocal correlation is inherently related to its
application. We address the question as to how many observers can share the
nonlocal advantage of quantum coherence (NAQC) in a $(d\times d)$-dimensional
state, where $d$ is a prime or a power of a prime. We first analyze the
trade-off between disturbance and information gain of the general
$d$-dimensional unsharp measurements. Then in a scenario where multiple Alices
perform unsharp measurements on one party of the state sequentially and
independently and a single Bob measures coherence of the conditional states on
the other party, we show that at most one Alice can demonstrate NAQC with Bob.
This limit holds even when considering the weak measurements with optimal
pointer states. These results may shed light on the interplay between nonlocal
correlations and quantum measurements on high-dimensional systems and the
hierarchy of different quantum correlations.
