Pic assist:
It appears that the derailleur is mounted on an integral hanger. Depending on how old the frame is, the hanger may be unthreaded (Simplex derailleurs did not require a threaded hanger). If the hanger is threaded, replacing the derailleur should be a matter of removing the old one and mounting and adjusting the new one. Depending on the specific dropout and replacement derailleur, some filing of the hanger may be needed to properly mount the replacement. Be aware that, unlike other derailleurs, Simplex mounting bolts are accessed from the back side of the dropout.
If the hanger is unthreaded, you can use a tap to cut 10mm x 1mm threads in the hanger to mount a non-Simplex derailleur.