The most common and most likely answer to this crossword clue is the 13 letter word NOSTALGICALLY
I've seen this crossword clue in Financial Times
N
O
S
T
A
L
G
I
C
A
L
L
Y
Buddy explains!
The straight part
We know that "looking back to past with fondness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case looking back to past with fondness = nostalgically.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.