Asian language group cheers up the writer's mood (10)
I believe the answer is:
indicative
'mood' is the definition.
(the indicative mood in grammar)
'asian language group cheers up the writer's' is the wordplay.
'asian language group' becomes 'indic' (I can't justify this - if you can you should believe this answer much more).
'cheers' becomes 'ta' (both can informally mean thank you).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'the writer's' becomes 'I've' (the writer of the crossword).
'ta' back-to-front is 'at'.
'indic'+'at'+'ive'='INDICATIVE'
Can you help me to learn more?
(Other definitions for indicative that I've seen before include "Serving as a sign" , "mood" .)