The most common and most likely answer to this crossword clue is the 6 letter word DATING
I've seen this crossword clue in Financial Times
D
A
T
I
N
G
More clues leading to the result DATING
- Introducing Dave, about to interest new girlfriend in romance
- Seeing American lawyer can start to grind
- Becoming old-fashioned like regular sweethearts?
- Father can start to go courting
- Saying when?
- An item rushing 25 10
- Fixing time for courting
- Finding out how long something has existed in a relationship?
- Diamonds on a ring becoming old-fashioned
- Courting daughter with giant fiddle
Buddy explains!

The straight part
We know that "Becoming old-fashioned" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case becoming old-fashioned = dating.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 DATING mean?
DATING verb- To note the time or place of writing or executing; to express in an instrument the time of its execution.
- To note or fix the time of (an event); to give the date of.
- To determine the age of something.
- To take (someone) on a date, or a series of dates.
- (by extension) To have a steady relationship with; to be romantically involved with.
- (by extension) To have a steady relationship with each other; to be romantically involved with each other.
- To make or become old, especially in such a way as to fall out of fashion, become less appealing or attractive, etc.
- (with from) To have beginning; to begin; to be dated or reckoned.
- A form of romantic courtship typically between two individuals with the aim of assessing the other's suitability as a partner in an intimate relationship or as a spouse.
- An estimation of the age of an artifact, biological vestige, linguistic usage, etc.
- The setting of a date on which an event or transaction is to take place or take effect.