In this Letter of Intent, the STAR collaboration proposes a path to evolve STAR into a major experiment, referred to as eSTAR, at a possible future Electron-Ion Collider (EIC) at Brookhaven National Laboratory, eRHIC. A core component of this plan is a suite of optimized detector upgrades to maintain and extend the existing low-mass mid-central rapidity tracking and particle-identification capabilities towards forward rapidity to enable the precision deep-inelastic-scattering measurements that form the experimental foundation of the EIC science program. This Letter of Intent is submitted in response to a May 2013 charge by BNL Associate Laboratory Director Berndt Mueller, which is reproduced in the Appendix to this Letter.