  We report the discovery of a close-in ($P_{\mathrm{orb}} =
3.349\:\mathrm{days}$) warm Neptune with clear transit timing variations (TTVs)
orbiting the nearby ($d=47.3\:\mathrm{pc}$) active M4 star, TOI-2015. We
characterize the planet's properties using TESS photometry, precise
near-infrared radial velocities (RV) with the Habitable-zone Planet Finder (HP)
Spectrograph, ground-based photometry, and high-contrast imaging. A joint
photometry and RV fit yields a radius $R_p~=~3.37_{-0.20}^{+0.15}
\:\mathrm{R_\oplus}$, mass $m_p~=~16.4_{-4.1}^{+4.1}\:\mathrm{M_\oplus}$, and
density $\rho_p~=~2.32_{-0.37}^{+0.38} \:\mathrm{g cm^{-3}}$ for TOI-2015b,
suggesting a likely volatile-rich planet. The young, active host star has a
rotation period of $P_{\mathrm{rot}}~=~8.7 \pm~0.9~\mathrm{days}$ and
associated rotation-based age estimate of $1.1~\pm~0.1\:\mathrm{Gyr}$. Though
no other transiting planets are seen in the TESS data, the system shows clear
TTVs of super period $P_{\mathrm{sup}}~\approx~430\:\mathrm{days}$ and
amplitude $\sim$$100\:\mathrm{minutes}$. 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 resonance
-- cannot be conclusively excluded without further observations. Assuming a 2:1
resonance in the joint TTV-RV modeling suggests a mass of
$m_b~=~13.3_{-4.5}^{+4.7}\:\mathrm{M_\oplus}$ for TOI-2015b and
$m_c~=~6.8_{-2.3}^{+3.5}\:\mathrm{M_\oplus}$ 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.
