We present a search for long-lived particles (LLPs) produced in association with a $\mathrm{Z}$ boson. The search is performed with data from 13~\mathrm{TeV} proton-proton collisions recorded by the CMS experiment during $2016-2018$, corresponding to an integrated luminosity of 117~\mathrm{fb}^{-1}. The LLPs are assumed to decay into a pair of standard model fermions inside the tracker volume, which results in displaced jets. A trigger and selections based on $\mathrm{Z}$ boson decays to electron or muon pairs provide sensitivity to light (15~\mathrm{GeV} or less) LLPs, which have up to now been difficult to access. Decays of LLPs are selected by requiring the presence of displaced jets which are identified using information from the CMS tracking system. The results are interpreted in the context of exotic decays of the Higgs boson to LLPs ($\mathrm{H} \to \mathrm{S}\mathrm{S}$). The search is sensitive to branching fractions $\mathcal{B}$($\mathrm{H} \to \mathrm{S}\mathrm{S}$) of $4-5\%$ (less than $20\%$) for LLP masses of 40 (15)~\mathrm{GeV} and mean proper decay lengths of 10-100~\mathrm{mm} (10-50~\mathrm{mm}).

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