The most common and most likely answer to this crossword clue is the 7 letter word DRUDGES
I've seen this crossword clue in The Times
D
R
U
D
G
E
S
Buddy explains!

The straight part
We know that "skivvies" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case skivvies = drudges.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 DRUDGES mean?
DRUDGES noun- A person who works in a low servile job.
- Someone who works for (and may be taken advantage of by) someone else.