To clarify the above . . .
There has been, as yet, not the slightest hint of a criminal prosecution of any sort being brought against Prince Andrew, whether that be in the UK (where he lives), in Australia (where his accuser lives) or in the USA (where the current civil proceedings are taking place). So there's currently absolutely no possibility whatsoever of Prince Andrew being sentenced to custody or to anything else. As in the UK, a civil court in the USA can only award damages to a claimant.
A post above refers to a 'private prosecution' but such (criminal) prosecutions are extremely unusual, and difficult to pursue, almost anywhere in the world. In particular, in New York state (where the current civil proceedings are taking place), the District Court ruled in 2002 that "private prosecutions by interested parties or their attorneys present inherent conflicts of interest which violate defendants' due process rights".
Civil cases aren't 'private prosecutions'. They're simply a claim for compensation for being wronged. In civil law (almost anywhere in the world) a claimant only has to show that their account of the facts is true based upon 'the balance of probabilities'. It's far harder for the prosecution to succeed in criminal proceedings where (again, almost anywhere in the world) they have to prove their case 'beyond reasonable doubt'. [That's why, for example, a Scottish civil court was able to rule that the footballer David Goodwillie had committed rape, and order him to pay £100k in compensation to the victim, but the Procurator Fiscal was unable to proceed with a criminal case against him].