The most common and most likely answer to this crossword clue is the 4 letter word GAMP
I've seen this crossword clue in The Times
G
A
M
P
Buddy explains!
The straight part
We know that "brolly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case brolly = gamp.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 GAMP mean?
GAMP noun- An umbrella.