One’s right under, that’s strange (5)
I believe the answer is:
alien
'strange' is the definition.
(synonyms)
'one's right under' is the wordplay.
'one' becomes 'a'.
'right' becomes 'lien' (I've seen this before).
'under' is a charade indicator (letters next to each other).
'a'+'lien'='ALIEN'
'that's' acts as a link.
(Other definitions for alien that I've seen before include "repugnant" , "extraneous" , "exciting film based in space" , "Belonging to a foreign country" , "Clanger?" .)