The most common and most likely answer to this crossword clue is the 8 letter word CURATING
I've seen this crossword clue in The Times
C
U
R
A
T
I
N
G
Buddy explains!
The straight part
We know that "Looking after" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case looking after = curating.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 CURATING mean?
CURATING verb- To act as a curator for.
- To apply selectivity and taste to, as a collection of fashion items or web pages.
- To work or act as a curator.