The most common and most likely answer to this crossword clue is the 4 plus 4 letter word BOAT TRIP
I've seen this crossword clue in Financial Times
B
O
A
T
T
R
I
P
Buddy explains!
The straight part
We know that "What seasick British patriot may be on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what seasick british patriot may be on = boat trip.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.