The most common and most likely answer to this crossword clue is the 7 letter word DIDDUMS
I've seen this crossword clue in The Times
D
I
D
D
U
M
S
More clues leading to the result DIDDUMS
Buddy explains!

The straight part
We know that "There there!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case there there! = diddums.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 DIDDUMS mean?
DIDDUMS interjection- A term of commiseration to a child who has suffered a mildly painful situation.
- (by extension) A sarcastic commiseration to somebody seen to be complaining too much about hurt feelings.