The most common and most likely answer to this crossword clue is the 8 letter word RENOVATE
I've seen this crossword clue in Financial Times
R
E
N
O
V
A
T
E
Buddy explains!

The straight part
We know that "To give a facelift to" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to give a facelift to = renovate.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 RENOVATE mean?
RENOVATE verb- To renew; to revamp something to make it look new again.
- To restore to freshness or vigor.