  Given a finite field $\mathbb F_q$, a positive integer $n$ and an $\mathbb
F_q$-affine space $\mathcal A\subseteq \mathbb F_{q^n}$, we provide a new bound
on the sum $\sum_{a\in \mathcal A}\chi(a)$, where $\chi$ a multiplicative
character of $\mathbb F_{q^n}$. We focus on the applicability of our estimate
to results regarding the existence of special primitive elements in $\mathbb
F_{q^n}$. In particular, we obtain substantial improvements on previous works.
