The most common and most likely answer to this crossword clue is the 6 letter word QUEASY
I've seen this crossword clue in The Daily Telegraph
Q
U
E
A
S
Y
More clues leading to the result QUEASY
- Queen comfortable, or nauseous?
- Inclined to chuck wandering herd out of Hardyesque novel
- Two separate points in landing-place could make you groggy
- Peculiar in technique as youngster
- Feeling unwell, queen needs a piece of cake?
- Choppy sea for one in landing-place making one nauseous
- Queen relaxed the sick
- Feeling anxious, having lost ID in quayside scuffle
Buddy explains!

The straight part
We know that "groggy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case groggy = queasy.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 QUEASY mean?
QUEASY adjective- Experiencing or causing nausea or uneasiness, often characterized by an unsettled stomach.
- Easily troubled; squeamish.