If Business Property Relief and Agricultural Property Relief apply to the same property, I know APR has priority but I am wondering if you can apply both for the same asset?
Yes its possible in case of 1) an unincorporated farming business and 2) if shares are held in a farming business. APR will be available on the agricultural value and BPR will be available for the business assets.
For further reading and examples you can refer to Kaplan text chapter 12.