The most common and most likely answer to this crossword clue is the 3 plus 5 letter word TIA MARIA
I've seen this crossword clue in Financial Times
T
I
A
M
A
R
I
A
More clues leading to the result TIA MARIA
- Timid at first, I'm on song, getting a drink
- Dry in the morning; before start of afternoon, Italian’s knocked back liqueur
- Tiny boy penning a song for a drink
- Formal bling worn by mum holding a single drink
- Drink, Italian, brought back by a girl
- Drink one with a girl after time
- Booze time? Hoskins is getting a flipping excellent drop of red
- With no source of sugar, amrita is a poor drink
- Note a sailing haunt banning new liqueur
- Drink most of time, welcoming a song
Buddy explains!

The straight part
We know that "Drink" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case drink = tia maria.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.