  We study deformations of a pair of a $\mathbb{Q}$-Fano $3$-fold $X$ with only
terminal singularities and its elephant $D \in |{-}K_X|$. We prove that, if
there exists $D \in |{-}K_X|$ with only isolated singularities, the pair
$(X,D)$ can be deformed to a pair of a $\mathbb{Q}$-Fano $3$-fold with only
quotient singularities and a Du Val elephant. When there are only non-normal
elephants, we reduce the existence problem of such a deformation to a local
problem around the singular locus of the elephant. We also give several
examples of $\mathbb{Q}$-Fano $3$-folds without Du Val elephants.
