The most common and most likely answer to this crossword clue is the 6 plus 4 letter word MEMORY LANE
I've seen this crossword clue in The Times
M
E
M
O
R
Y
L
A
N
E
More clues leading to the result MEMORY LANE
Buddy explains!
The straight part
We know that "way of looking back" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case way of looking back = memory lane.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.