The most common and most likely answer to this crossword clue is the 6 letter word SMARMY
I've seen this crossword clue in The Times
S
M
A
R
M
Y
More clues leading to the result SMARMY
- Obsequious in writing about host
- Obsequious sergeant-major and his sphere of influence
- Oily stuff’s running to the left of me
- Being obsequious would put Mrs May off
- Ingratiating school-mistress in borders of Surrey
- Obsequious warrant officer with the forces
- Bootlicking troops trailing officer
- Bootlicking Sergeant-Major leading his men?
- Obsequious host following modern miss around
- Well-oiled host supports kinky activity?
Buddy explains!

The straight part
We know that "Obsequious" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case obsequious = smarmy.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 SMARMY mean?
SMARMY adjective- Falsely earnest, smug, or ingratiating.
- Unctuous, greasy, as hair from pomade