The most common and most likely answer to this crossword clue is the 7 letter word PROCEED
I've seen this crossword clue in Independent
P
R
O
C
E
E
D
Buddy explains!

The straight part
We know that "advance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case advance = proceed.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 PROCEED mean?
PROCEED verb- To move, pass, or go forward or onward; to advance; to carry on
- To pass from one point, topic, or stage, to another.
- To come from; to have as its source or origin.
- To go on in an orderly or regulated manner; to begin and carry on a series of acts or measures; to act methodically
- To be transacted; to take place; to occur.
- (of a rule) To be applicable or effective; to be valid.
- To begin and carry on a legal process.
- To take an academic degree.