The most common and most likely answer to this crossword clue is the 5 plus 4 plus 3 plus 5 letter word SHORT BACK AND SIDES
I've seen this crossword clue in The Times
S
H
O
R
T
B
A
C
K
A
N
D
S
I
D
E
S
Buddy explains!
The straight part
We know that "More than just a trim" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case more than just a trim = short back and sides.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.