Relaxed at home with kind American student (8)
I believe the answer is:
informal
'relaxed' is the definition.
(informal can mean relaxed or casual)
'home with kind american student' is the wordplay.
'home' becomes 'in' (to be in is to be (at) home).
'with' means one lot of letters go next to another.
'kind' becomes 'form' (synonyms).
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'student' becomes 'L' (as in L-plates for learner drivers).
'in'+'form'+'a'+'l'='INFORMAL'
'at' acts as a link.
(Other definitions for informal that I've seen before include "Casual or unofficial" , "If normal, be casual and without ceremony" , "Casual, free and easy" , "Unofficial, relaxed" , "Cosy -- loose" .)