Started new pill for mood. Foot drop. Will the nerve recover?

Not associated. The drug and foot drop probably not associated consult your physician.
Foot drop. Patients have a high chance at recovery. Depending on the level of injury the recovery times can be different. Most medications do not cause foot drop, however a good exam will pinpoint the cause, diagnosis and treatment plan. Best wishes!
Should. If the medication caused the foot drop it should return to nomal with stopping the drug.