Sickly character called out for drink (5,3)

I believe the answer is:

green tea

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

'drink' is the definition.
(type of tea)

'sickly character called out' is the wordplay.
'sickly' becomes 'green' (I am not sure about this - if you are sure you should believe this answer much more).
'character' becomes 'T'.
'called out' indicates a 'sounds like' (homophone) clue.
't' is a homophone of 'tea'.
'green'+'tea'='GREEN TEA'

'for' acts as a link.

Can you help me to learn more?

(Other definitions for green tea that I've seen before include "'Asian herbal drink (5,3)'" , "Food at the golf club" , "Brewed" , "Hot drink - teenager (anag)" , "Beverage" .)

I've seen this clue in The Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.