The most common and most likely answer to this crossword clue is the 5 letter word SPANK
S
P
A
N
K
Buddy explains!

The straight part
We know that "go at a lick" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case go at a lick = spank.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 SPANK mean?
SPANK noun- An instance of spanking, separately or part of a multiple blows-beating; a smack, swat, or slap.
- A slapping sound, as produced by spanking.
- To beat, smack or slap a person's buttocks, with the bare hand or other object, as punishment, gesture, or form of sexual interaction.
- To soundly defeat, to trounce.
- To hit very hard
- To move rapidly.