Foreign cousin’s reserve suppressing an air of carelessness (11)

I believe the answer is:

insouciance

I'm a little stuck... Click here to teach me more about this clue!

'air of carelessness' is the definition.
'insouciance' can be an answer for 'carelessness' (thesaurus). I'm not certain of the 'air of' bit.

'foreign cousin's reserve suppressing an' is the wordplay.
'foreign' indicates an anagram (foreign order of the letters).
'reserve' becomes 'ice' (both can mean aloofness).
'suppressing' indicates putting letters inside.
'ice' enclosing 'an' is 'iance'.
'cousin' with letters rearranged gives 'insouc'.
'insouc'+'iance'='INSOUCIANCE'

Can you help me to learn more?

(Other definitions for insouciance that I've seen before include "Casual unconcern" , "Lack of concern" .)

I've seen this clue in The Independent.

Want a hint initially instead of a full solution? Install my app