The estimation of extreme quantiles requires adapted methods to extrapolate beyond the largest observation of the sample. Extreme-value theory provides a mathematical framework to tackle this problem together with statistical procedures based on the estimation of the so-called tail-index describing the distribution tail. We focus on heavy-tailed distributions and consider the case where the observations at hand are related to statistical models with different tail-index, a.k.a. as a mixture of heavy-tail models, and for conservative risk management reasons, we are interested in the largest tail-index. In such a mixture situation, usual extreme-value estimators suffer from a strong bias, which may induce in turn a strong bias when quantifying tail risk in this mixture model. We propose several methods to mitigate this bias under mild assumptions on the mixture distribution. Their asymptotic properties are established and their finite sample performance is illustrated both on simulated and real financial data.