The most common and most likely answer to this crossword clue is the 4 letter word YANK
I've seen this crossword clue in The Times
Y
A
N
K
More clues leading to the result YANK
Buddy explains!

The straight part
We know that "tug" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tug = yank.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 YANK mean?
YANK noun- A sudden, vigorous pull (sometimes defined as mass times jerk, or rate of change of force).
- A masturbation session.
- To pull (something) with a quick, strong action.
- To remove from distribution.
- A Yankee.