[en] GRB 110721A was detected by the Gamma-ray Burst Monitor and the Large Area Telescope (LAT) on board the Fermi satellite and the Gamma-ray Burst Polarimeter on board the IKAROS solar mission. Previous analysis of this burst showed: (i) a linear polarization signal with position angle stable (${\mathrm{\varphi <!--\; ??\; -->}}_p={160}^{\circ <!--\; ???\; -->}\pm <!--\; ??\; -->11$) and high degree of $\mathrm{\Pi <!--\; ??\; -->}={84}_{-<!--\; ???\; -->28}^{+16}\mathrm{\%<!--\; \%\; -->}$, (ii) an extreme peak energy of a record-breaking 15 ± 2 MeV, and (iii) a subdominant prompt thermal component observed right after the onset of this burst. In this paper, the LAT data around the reported position of GRB 110721A are analyzed with the most recent software and then, the LAT light curve above 100 MeV is obtained. The LAT light curve is modeled in terms of adiabatic early-afterglow external shocks when the outflow propagates into a stellar wind. Additionally, we discuss the possible origins and also study the implications of the early-afterglow external shocks on the extreme peak energy observed at 15 ± 2 MeV, the polarization observations, and the subdominant prompt thermal component.