A steady-state magneto-optical trap (MOT) of fermionic strontium atoms operating on the 7.5 kHz-wide ${^1mathrm{S}_0} - {^3mathrm{P}_1}$ transition is demonstrated. This MOT features $8.4 times 10^{7}$ atoms, a loading rate of $1.3times 10^{7}$atoms/s, and an average temperature of 12 $mu$K. These parameters make it well suited to serve as a source of atoms for continuous-wave superradiant lasers operating on strontiums mHz-wide clock transition. Such lasers have only been demonstrated using pulsed Sr sources, limiting their range of applications. Our MOT makes an important step toward continuous operation of these devices, paving the way for continuous-wave active optical clocks.