The most common and most likely answer to this crossword clue is the 9 letter word THEREUPON
I've seen this crossword clue in The Daily Telegraph
T
H
E
R
E
U
P
O
N
More clues leading to the result THEREUPON
- Re-open hut, possibly, with that
- Edging away, other troops leading at that point
- True? Phone to find out immediately
- Article on voucher company dismissed straight away
- Order punt over here, immediately!
- At that point three moved aloft, with no going back
- … immediately after that putting her note up for revision
- Instantly combustible phone? True
- Word of sympathy raised by side of pitch immediately
- Following that article about conversion of pound, Germany moved out
Buddy explains!

The straight part
We know that "immediately after that" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case immediately after that = thereupon.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 THEREUPON mean?
THEREUPON adverb- Upon that; thereon.
- In consequence, or by reason, of that; therefore.
- Following that; forthwith; in sequence, but not necessarily in consequence.