The most common and most likely answer to this crossword clue is the 5 letter word DOSED
I've seen this crossword clue in The Times
D
O
S
E
D
More clues leading to the result DOSED
- Given shot, daughter does shot
- Computer system news chief’s given a shot
- Some Parisian turning up after party drugged
- Given medicine, does drunk do without love?
- Given drug in parties, took drug then died
- 1a has change of heart being medicated
- Drugged, but oddly steady after party
- Given medicine, slept half-heartedly
- Given a drug in rave-up, wanting new thrill
- Drops tend oddly to get prescribed
Buddy explains!

The straight part
We know that "given a shot" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case given a shot = dosed.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.