Will the new owner honour a promotion I was promised before the sale?

This depends heavily on how firm that promise actually was, and a new owner isn't automatically bound by every conversation the old ownership had with you. If the promotion was a genuinely finalized commitment — confirmed in writing, tied to a specific date or condition that's already been met, or otherwise a real, enforceable term of your employment rather than an aspiration discussed informally — that's a term of your job the new owner generally steps into along with everything else, especially where your employment is treated as continuous through the sale.

If it was more of an informal discussion, or something contingent on approvals or budget that never happened, a new owner has much more legitimate room to revisit it as part of its own plans for the business, since it wasn't a binding commitment to begin with. The honest answer is that the strength of your position tracks the strength of the original promise — vague verbal assurances are harder to enforce than a signed letter or an email confirming specific terms.

Gather whatever documentation exists, and raise it directly with the new owner rather than assuming either that it's guaranteed or that it's automatically void.