The most common and most likely answer to this crossword clue is the 4 letter word COST
I've seen this crossword clue in Financial Times
C
O
S
T
More clues leading to the result COST
Buddy explains!

The straight part
We know that "Expense" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case expense = cost.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 COST mean?
COST verb- To incur a charge of; to require payment of a (specified) price.
- To cause something to be lost; to cause the expenditure or relinquishment of.
- To require to be borne or suffered; to cause.
- To calculate or estimate a price.
- Amount of money, time, etc. that is required or used.
- A negative consequence or loss that occurs or is required to occur.
- Manner; way; means; available course; contrivance.
- Quality; condition; property; value; worth; a wont or habit; disposition; nature; kind; characteristic.
- A rib; a side.
- A cottise.