We report the discovery of a close-in (Porb=3.349days) warm Neptune with clear transit timing variations (TTVs) orbiting the nearby (d=47.3pc) active M4 star, TOI-2015. We characterize the planet's properties using Transiting Exoplanet Survey Satellite (TESS) photometry, precise near-infrared radial velocities (RVs) with the Habitable-zone Planet Finder Spectrograph, ground-based photometry, and high-contrast imaging. A joint photometry and RV fit yields a radius Rp=3.37_-0.20_^+0.15^R_{Earth}, mass mp=16.4-4.1_^+4.1^M_{Earth}, and density {rho}p=2.32-0.37_^+0.38^g/cm^3^ for TOI-2015 b, suggesting a likely volatile-rich planet. The young, active host star has a rotation period of Prot=8.7+/-0.9days and associated rotation-based age estimate of 1.1+/-0.1Gyr. Though no other transiting planets are seen in the TESS data, the system shows clear TTVs of super-period Psup~430days and amplitude ~100min. After considering multiple likely period-ratio models, we show an outer planet candidate near a 2:1 resonance can explain the observed TTVs while offering a dynamically stable solution. However, other possible two-planet solutions --including 3:2 and 4:3 resonances-- cannot be conclusively excluded without further observations. Assuming a 2:1 resonance in the joint TTV-RV modeling suggests a mass of m_b_=13.3_-4.5_^+4.7^M_{Earth} for TOI-2015 b and m_c=6.8_-2.3_^+3.5^M_{Earth}_ for the outer candidate. Additional transit and RV observations will be beneficial to explicitly identify the resonance and further characterize the properties of the system.