We have imported goods into the UK (free circulation) from the Far East and paid duty on them. Now that the EU is a 3rd country, can we claim back any of this duty? Several years ago this would have come under IPR (Inward Processing Relief) type procedures.
It isn’t clear from the question what the grounds or basis for claiming repayment of customs duty would be in the circumstances referred to. The UK is still part of the EU, and therefore the applicable customs duty rates on imports remain as per the current Customs Tariff.
In the event of the UK leaving the EU without a deal the UK Government has prepared temporary customs tariff rates that would take effect from day 1 of that event. They would not apply retrospectively.
Similarly, in the event of a no deal exit, the UK plans to replicate in UK law many existing EU customs procedures such as Inward Processing. However, these Special Procedures (as they are referred to in EU law) are currently still in place under EU law.