The most common and most likely answer to this crossword clue is the 13 letter word HYPERESTHESIA
H
Y
P
E
R
E
S
T
H
E
S
I
A
Buddy explains!
The straight part
We know that "Trump’s excessive sensitivity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case trump’s excessive sensitivity = hyperesthesia.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 HYPERESTHESIA mean?
HYPERESTHESIA noun- Unusual or pathological sensitivity of the skin or of a particular sense.