Encounter of some ethical significance (4)
I believe the answer is:
meet
'encounter' is the definition.
(I know that come across can be written as meet)
'of some ethical significance' is the wordplay.
'of' indicates the answer is hidden within the clue.
'MEET' is hidden within 'some ethical significance'.
(Other definitions for meet that I've seen before include "Appropriate" , "Proper; touch" , "Assemble" , "Come face to face with - it is proper" , "Bump into" .)