The most common and most likely answer to this crossword clue is the 7 letter word YOUTUBE
I've seen this crossword clue in Independent
Y
O
U
T
U
B
E
Buddy explains!
The straight part
We know that "I’ll look after your videos" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case i’ll look after your videos = youtube.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 YOUTUBE mean?
YOUTUBE noun- Any website that allows users to upload content, particularly YouTube itself.
- A small video that can be viewed online, particularly one hosted on YouTube.