Half-hearted boost popular with old Asian islander (8)
I believe the answer is:
filipino
'asian islander' is the definition.
'filipino' can be an answer for 'islander' (I've seen this before). I'm not certain of the 'asian' bit.
'half-hearted boost popular with old' is the wordplay.
'half hearted boost' becomes 'filip' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'popular' becomes 'in' ('in' can mean trendy).
'with' means one lot of letters go next to another.
'old' becomes 'o' (abbreviation).
'filip'+'in'+'o'='FILIPINO'
Can you help me to learn more?
(Other definitions for filipino that I've seen before include "Native of islands, capital Manila" , "Asian" , "Person from the Philippines" , "Nationality of citizen of Manila" , "islander" .)