We report on the realization of a magneto-optical trap (MOT) for metastable strontium operating on the 2.92 $mu$m transition between the energy levels $5s5p~^3mathrm{P}_2$ and $5s4d~^3mathrm{D}_3$. The strontium atoms are initially captured in a MOT operating on the 461 nm transition between the energy levels $5s^2~^1mathrm{S}_0$ and $5s5p~^1mathrm{P}_1$, prior to being transferred into the metastable MOT and cooled to a final temperature of 6 $mu$K. Challenges arising from aligning the mid-infrared and 461 nm light are mitigated by employing the same pyramid reflector to realize both MOTs. Finally, the 2.92 $mu$m transition is used to realize a full cooling sequence for an optical lattice clock, in which cold samples of $^{87}mathrm{Sr}$ are loaded into a magic-wavelength optical lattice and initialized in a spin-polarized state to allow high-precision spectroscopy of the $5s^2~^1mathrm{S}_0$ to $5s5p~^3mathrm{P}_0$ clock transition.