Zero-age main-sequence stars (ZAMSs) are considered to have enormous starspots and show strong chromospheric emission lines because of their strong surface magnetic field. Marsden, Carter, \& Donati (2009, MNRAS, 399, 888) investigated Ca II infrared triplet (IRT ; $\lambda 8498, 8542, 8662 \, \mathrm{\angstrom}$) emission line of ZAMSs in young open clusters, IC 2391 ($50\,\mathrm{Myr}$) and IC 2602 ($30\,\mathrm{Myr}$). The objects having smaller Rossby number ($N_{\rm R} \equiv$ rotational period $P$ / convective turnover time $\tau_{\rm c}$) tend to show strong emission lines. For the stars with $\log N_{\rm R} \geq -0.8$, $R^{\prime}_{\lambda 8542}$, the ratio of the surface flux of the Ca\,\emissiontype{II} IRT emission line at $\lambda 8542\,\mathrm{\angstrom}$ to the stellar bolometric luminosity, increases with decreasing $N_{\rm R}$ (the unsaturated regime). For the stars with $\log N_{\rm R} \leq -0.8$, $R^{\prime}_{\lambda 8542}$ is constant (the saturated regime). We discuss the dynamo activities of ZAMSs with their periodic light variation caused by a starspot and with the strength of the chromospheric emission lines. The amplitudes of the light curves of 46 ZAMSs in IC 2391 and IC 2602 were measured with {\it TESS} photometric data. The light curves can be grouped into the following four categories; single frequency, double-dipped, beater, and irregular variability. The amplitudes of the light curves are $0.001-0.145\,\mathrm{mag}$, which are similar to those of ZAMSs in Pleiades (Rebull et al. 2016, AJ, 152, 133). The starspot coverages are $0.1-17\%$. It is known that the solar-type superflare stars with the large amplitude of the light curve have strong Ca II IRT emission line (Notsu et al. 2015, PASJ, 67, 33). We found that the light variations and $R^{\prime}_{\lambda 8542}$ of the ZAMSs are as large as those of the most active superflare stars and three orders larger than those of the Sun. It is suggested that the high magnetic activity similar to that of the Sun continues from $30\, \mathrm{Myr}$ old. ZAMSs with single frequency in the light curve tend to have both large light variation, indicating large spot coverage, and saturated $R^{\prime}_{\rm \lambda 8542}$. ZAMSs with irregular variability have small spot coverage ($\lesssim 1 \%$) and small $R^{\prime}_{\rm \lambda 8542}$. We also detected $32$ flares in the {\it TESS} light curves of 14 ZAMSs. The energy of the flares are estimated as $\sim 10^{33}-10^{35}\,\mathrm{erg}$, which are comparable to the energy of superflare.