The most common and most likely answer to this crossword clue is the 9 letter word EMBROIDER
I've seen this crossword clue in Financial Times
E
M
B
R
O
I
D
E
R
More clues leading to the result EMBROIDER
- Exaggerate European doctor touching designer up
- Add fanciful details to glowing piece about French King and daughter
- Elaborately sew Christian up during his fast day
- Dress up bride more elaborately
- Do some needling, upsetting bored emir
- Ornament fashion designer turned into coal
- Exaggerate stitch
- Add imaginary detail to what one with needle does?
- Mark’s brother stuffing duck? That’s to provide embellishment
- Elaborate stitch
Buddy explains!

The straight part
We know that "to provide embellishment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to provide embellishment = embroider.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 EMBROIDER mean?
EMBROIDER verb- To stitch a decorative design on fabric with needle and thread of various colours.
- To add imaginary detail to a narrative to make it more interesting or acceptable.