The most common and most likely answer to this crossword clue is the 6 letter word PROWLS
I've seen this crossword clue in The Guardian
P
R
O
W
L
S
Buddy explains!
The straight part
We know that "What stalker does" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what stalker does = prowls.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 PROWLS mean?
PROWLS verb- To rove over, through, or about in a stealthy manner; especially, to search in, as for prey or booty.
- To idle; to go about aimlessly.
- To collect by plunder.