Summary: Let \(\{Z_t\}_{t\geq 0}\) be a Lévy process with Lévy measure \(\nu \), and let \(\tau (t)=\int _{0}^{t}r(u)\,u\), where \(\{r(t)\}_{t\geq 0}\) is a positive ergodic diffusion independent from \(Z\). Based upon discrete observations of the time-changed Lévy process \(X_t:=Z_{\tau _{t}}\) during a time interval \([0,T]\), we study the asymptotic properties of certain estimators of the parameters \(\beta (\varphi ):= \int \varphi (x)\nu (d x)\), which in turn are well known to be the building blocks of several nonparametric methods such as sieve-based estimation and kernel estimation. Under uniform boundedness of the second moments of \(r\) and conditions on \(\varphi\) necessary for the standard short-term ergodic property lim\(_{t\rightarrow 0}\) E \(\varphi (Z_{t})/t=\beta (\varphi )\) to hold, consistency and asymptotic normality of the proposed estimators are ensured when the time horizon \(T\) increases in such a way that the sampling frequency is high enough relative to \(T\).