"Pede Claudo" is an abbreviated reference to the Latin phrase "pede poena claudo" which translates to "punishment comes limping." This can be attributed to Quintus Horatius Flaccus (or more simply, Horace), the Latin lyric poet and satirist who wrote under the reign of Augustus.
This phrase arrives in chapter two of the novel, as Mr. Utterson walks home with "a very heavy heart" and considers what information Mr. Hyde must have in order to be able to blackmail Dr. Jekyll. Mr. Utterson comments that, "in the law of God, there is no statute of limitations." It, thus, must be some old disgrace or sin that Mr. Hyde is dragging up, resulting in the "punishment coming, PEDE CLAUDO." No one—not even Dr. Jekyll—may escape retribution, no matter how slow it may be to arrive.