I recently purchased an aircraft that was legally (and otherwise) airworthy. There is a visual inspection due (any private pilot can perform it) every 10 hours, but the ferry pilot may have overlooked this during the 18 hour ferry trip. The inspection due time has now gone over the 10 hour requirement. Are there additional requirements other than just inspecting again for compliance, or must something be submitted to the FAA as to report a non-compliance issue?
Each AD is specific (and unique) to the procedures and compliance outlined in the AD. If the AD does not say otherwise, all that is needed is to comply with it (do the inspection), and then make an entry in the maintenance log book, and you will be good to go.
I have never seen an AD that addresses circumstances when not previously complied with. For example, a Cessna 172 requires an inspection of the horizontal stabilizer spar; it does not matter if no one has done it for 45yrs. All that is needed is to do the required inspection and it is good to go :)