The most common and most likely answer to this crossword clue is the 10 letter word SYCOPHANCY
I've seen this crossword clue in The Guardian
S
Y
C
O
P
H
A
N
C
Y
Buddy explains!

The straight part
We know that "licking boots" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case licking boots = sycophancy.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 SYCOPHANCY mean?
SYCOPHANCY noun- The fawning behavior of a sycophant; servile flattery; fawningness.