  We study the effects of quenched disorder on electrons in a 3D nodal-line
semimetal. Disorder leads to significant renormalisations of the quasiparticle
properties due to ultraviolet processes, i.e., processes of scattering in a
large band of momenta, of the width exceeding the inverse mean free path. As a
result, observables such as the density of states and conductivity exhibit
singular behaviour in a broad range of disorder strengths, excluding a small
vicinity of the singular point. We find that, for example, the density of
quasiparticle states diverges as a function of the disorder strength $g$ as
$\rho(g,E)\propto |g_c(E)-g|^{-2}|E|$ for $g$ smaller than the critical value
$g_c(E)$ and crosses over to a constant for $g$ very close to $g_c(E)$, where
$E$ is the quasiparticle energy. For certain disorder symmetries, a 3D
disordered nodal-line semimetal can be mapped to a 2D metal with attractive
interactions. The described disorder-driven instabilities in such a nodal-line
semimetal are mapped to Cooper and exciton-condensation instabilities in a 2D
metal. For other disorder symmetries, the respective instabilities are similar
but not exactly dual. We discuss experimental conditions favourable for the
observation of the described effects.
