The most common and most likely answer to this crossword clue is the 7 letter word SNIGGLE
S
N
I
G
G
L
E
Buddy explains!

The straight part
We know that "Fish for eels" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fish for eels = sniggle.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 SNIGGLE mean?
SNIGGLE verb- To chortle or chuckle; snicker (often used in contempt).
- To fish for eels by thrusting a baited hook into their dens.
- To catch by this means.
- To ensnare.
- To steal something of little value