The most common and most likely answer to this crossword clue is the 10 letter word NIT-PICKER
I've seen this crossword clue in Independent
N
I
T
-
P
I
C
K
E
R
More clues leading to the result NIT-PICKER
- Pound split by Italian page for fussy fault-finder
- Egg’s best served with endless butter for fussy type
- Critic: “It’s penny that should be contained in pound”
- Fusspot flipped can, and cream emptied easier
- Critic elected to return and watch entertaining play’s opening
- Drunkenly inept Rick is overly-fussy critic
Buddy explains!

The straight part
We know that "fussy type" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fussy type = nit-picker.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.