A method is presented to reconstruct charged particles with lifetimes between 10ps and 10ns, which considers a combination of their decay products and the partial tracks created by the initial charged particle. Using the Ξ- baryon as a benchmark, the method is demonstrated with simulated events and proton-proton collision data at s=13TeV, corresponding to an integrated luminosity of 2.0fb-1 collected with the LHCb detector in 2018. Significant improvements in the angular resolution and the signal purity are obtained. The method is implemented as part of the LHCb Run 3 event trigger in a set of requirements to select detached hyperons. This is the first demonstration of the applicability of this approach at the LHC, and the first to show its scaling with instantaneous luminosity.