The most common and most likely answer to this crossword clue is the 7 plus 5 letter word MELANIA TRUMP
I've seen this crossword clue in The Guardian
M
E
L
A
N
I
A
T
R
U
M
P
Buddy explains!
The straight part
We know that "Other half" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case other half = melania trump.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.