The number of ageing people with relapsing multiple sclerosis (RMS) is increasing. The efficacy of disease-modifying therapies (DMTs) for RMS declines with age. Also, older persons with MS may be more susceptible to infections, hospitalisations and malignancy. Aging people with MS have higher rates of comorbidities versus aged-matched controls, increasing the individual risk of disability. We review the therapeutic properties of cladribine tablets (CladT) in ageing people with RMS, with regard to their utility for allowing these individuals to cease continuous administration of a DMT (i.e. to act as an “exit therapy”). CladT is thought to be an immune reconstitution therapy, in that two short courses of oral treatment 1 year apart provide suppression of MS disease activity in responders that far outlasts the duration of treatment and post-treatment reductions in lymphocyte counts. Post hoc analyses, long-term follow-up of populations with RMS in randomised trials, and real-world evidence suggest that the efficacy of CladT is probably independent of age, although more data in the elderly are still needed. No clear adverse signals for lymphopenia or other adverse safety signals have emerged with increasing age, although immunosenescence in the setting of age-related “inflammaging” may predispose elderly patients to a higher risk of infections. Updating vaccination status is recommended, especially against pneumococci and herpes zoster for older patients, to minimise the risk of these infections. CladT may be a useful alternative treatment for ageing people with MS who often bear a burden of multiple comorbidities and polypharmacy and who are more exposed to the adverse effects of continuous immunosuppressive therapy.