The most common and most likely answer to this crossword clue is the 8 plus 6 letter word SPEAKERS CORNER
I've seen this crossword clue in Financial Times
S
P
E
A
K
E
R
S
C
O
R
N
E
R
More clues leading to the result SPEAKERS CORNER
Buddy explains!
The straight part
We know that "this part of Hyde Park" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case this part of hyde park = speakers corner.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.