The most common and most likely answer to this crossword clue is the 6 letter word GROGGY
I've seen this crossword clue in The Guardian
G
R
O
G
G
Y
More clues leading to the result GROGGY
Buddy explains!

The straight part
We know that "Dazed and unsteady/Dazed and unsteady" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dazed and unsteady/dazed and unsteady = groggy.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.
What does GROGGY mean?
GROGGY adjective- Slowed or weakened, as by drink, sleepiness, etc.
- Of a horse: bearing wholly on its heels when trotting.