The most common and most likely answer to this crossword clue is the 2 plus 4 plus 4 plus 2 letter word AS TIME GOES BY
I've seen this crossword clue in The Daily Telegraph
A
S
T
I
M
E
G
O
E
S
B
Y
More clues leading to the result AS TIME GOES BY
- Maybe egoists changing gradually
- Song bird relies on following it around
- Number you must remember while the clock’s ticking
- Boy with message – it comes out in film song
- Penned by a pen, some big shot penning end of nice old song
- 10 asked for it in due course
- Memorable song from Sam, yet Bogie’s furious
- Something sung in film when the enemy walks past?
Buddy explains!

The straight part
We know that "Memorable song" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case memorable song = as time goes by.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.