The most common and most likely answer to this crossword clue is the 9 letter word GLADSTONE
I've seen this crossword clue in The Times
G
L
A
D
S
T
O
N
E
More clues leading to the result GLADSTONE
- Young chap: good person enthralled by dead PM once
- Happy, having stumped one former Prime Minister
- PM's left without fellow ministers' support, ultimately
- Old prime minister pleased with gem
- Old British statesman delighted with jewel
- Prime Minister who used to be happy with weight?
- Happy to have stumped one English statesman
- Prime Minister pleased with extremely suspect individual
- Good chap’s sound for Prime Minister
- Good chaps with sound Prime Minister
Buddy explains!

The straight part
We know that "former Prime Minister" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case former prime minister = gladstone.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.