  This paper deals with the rate of convergence for the central limit theorem
of estimators of the drift coefficient, denoted $\theta$, for a
Ornstein-Uhlenbeck process $X \coloneqq \{X_t,t\geq0\}$ observed at high
frequency. We provide an Approximate minimum contrast estimator and an
approximate maximum likelihood estimator of $\theta$, namely
$\widetilde{\theta}_{n}\coloneqq {1}/{\left(\frac{2}{n}
\sum_{i=1}^{n}X_{t_{i}}^{2}\right)}$,
  and $\widehat{\theta}_{n}\coloneqq -{\sum_{i=1}^{n}
X_{t_{i-1}}\left(X_{t_{i}}-X_{t_{i-1}}\right)}/{\left(\Delta_{n} \sum_{i=1}^{n}
X_{t_{i-1}}^{2}\right)}$, respectively, where $ t_{i} = i \Delta_{n}$,
  $ i=0,1,\ldots, n $, $\Delta_{n}\rightarrow 0$.
  We provide Wasserstein bounds in
  central limit theorem for $\widetilde{\theta}_{n}$ and
$\widehat{\theta}_{n}$.
