The most common and most likely answer to this crossword clue is the 5 letter word BORIS
B
O
R
I
S
More clues leading to the result BORIS
- Foremost of Brexiteersis me
- On return steal one's man?
- Flipping mug is our leader
- Russian bishop’s prayer not working
- Johnson’s one sending soldiers in again
- Johnson perhaps sending soldiers in again
- Resigned minister pens ” I love to swap around”
- Nothing in ceremony to take end of Johnson?
- Stunt artist’s cry of distress, hanging around middle of wire upside down
- Man with Russian name is after British gold
Buddy explains!

The straight part
We know that "(recently) resigned minister" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case (recently) resigned minister = boris.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.