Reg. (EU) No 965/2012 NCO.GEN.145 point (b) states: ‘The operator shall implement […] (b) any relevant mandatory safety information issued by the Agency, including airworthiness directives.’
For NCO operations in the EU of a third country-registered aircraft, only the ADs mandated by the State of Registry apply — not the EASA ADs.
The word ‘relevant’ in point (b) of NCO.GEN.145 should be understood as ‘if applicable’ and allows to distinguish the different situation of an aircraft registered in an EASA Member State (ADs issued by EASA are relevant to these aircraft) as opposed to third-country registered aircraft, on which ADs mandated by the third-country State of Registry should be applied (refer to Annex 8 to the Chicago Convention).
It is common that ADs first issued by the State of Design are identically (or very similarly) issued or adopted by all States of Registry concerned. By European law (article 77 of Reg. (EU) 2018/1139, the so-called Basic Regulation (BR)), EASA performs State of Design functions on behalf of the EASA Member States.
Note 1: In accordance with Article 83-bis of the Chicago Convention, if agreed, the country where an aircraft is registered may transfer the oversight functions (including airworthiness) to the country of the aircraft operator. If, in such case, the operator is established or resides in an EASA Member State, EASA ADs are relevant to this aircraft.
Note 2: In accordance with article 77 of the BR, aircraft registered in an EASA Member State are required to comply with EASA-issued or adopted ADs. As per ED Decision No. 2/2003, EASA adopts ADs issued by the State of Design unless the Agency decides differently. Read more about ADs applicable to EASA Member State-registered aircraft in the EASA FAQ page on ADs.