Let $G$ be a finite permutation group on $Ω,$ a subgroup $K\leqslant G$ is called a fixer if each element in $K$ fixes some element in $Ω.$ In this paper, we characterize fixers $K$ with $|K|\geqslant |G_ω|$ for each primitive action of almost simple group $G$ with socle ${}^2G_2(q).$