The most common and most likely answer to this crossword clue is the 7 plus 4 letter word CHANGES GEAR
I've seen this crossword clue in The Sunday Telegraph
C
H
A
N
G
E
S
G
E
A
R
Buddy explains!
The straight part
We know that "Adjusts engagement/dresses differently" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case adjusts engagement/dresses differently = changes gear.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.