Kepler-51 is a <=1Gyr old Sun-like star hosting three transiting planets with radii ~6-9R_{Earth} and orbital periods ~45-130days. Transit timing variations (TTVs) measured with past Kepler and Hubble Space Telescope (HST) observations have been successfully modeled by considering gravitational interactions between the three transiting planets, yielding low masses and low mean densities (<=0.1g/cm^3^) for all three planets. However, the transit time of the outermost transiting planet Kepler-51d recently measured by the James Webb Space Telescope 10yr after the Kepler observations is significantly discrepant from the prediction made by the three-planet TTV model, which we confirmed with ground-based and follow-up HST observations. We show that the departure from the three-planet model is explained by including a fourth outer planet, Kepler-51e, in the TTV model. A wide range of masses (<=M_Jup) and orbital periods (<=10yr) are possible for Kepler-51e. Nevertheless, all the coplanar solutions found from our brute-force search imply masses <=10M_{Earth} for the inner transiting planets. Thus, their densities remain low, though with larger uncertainties than previously estimated. Unlike other possible solutions, the one in which Kepler-51e is around the 2:1 mean motion resonance with Kepler-51d implies low orbital eccentricities (<=0.05) and comparable masses (~5M{Earth}_) for all four planets, as is seen in other compact multiplanet systems. This work demonstrates the importance of long-term follow-up of TTV systems for probing longer-period planets in a system.