The most common and most likely answer to this crossword clue is the 5 letter word SCRIP
I've seen this crossword clue in The Times
S
C
R
I
P
Buddy explains!

The straight part
We know that "purse" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case purse = scrip.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 SCRIP mean?
SCRIP noun- A small medieval bag used to carry food, money, utensils etc.
- Small change.
- A scrap of paper.
- A document certifying possession of land, or in lieu of money.
- A voucher or token coin used in payrolls under the truck system; chit.
- Any substitute for legal tender that is produced by a natural person or private legal person and is often a form of credit.
- A share certificate.
- A medical prescription.