The most common and most likely answer to this crossword clue is the 5 letter word FIRST
I've seen this crossword clue in Financial Times
F
I
R
S
T
More clues leading to the result FIRST
- Commemorative envelope from factory drives production
- Primitive way to stop tree production
- Eldest child initially ready to tuck into left half of bonbon?
- Original equine measure — from the horse's mouth!
- Originally by mail, this voting system?
- Start January by visiting and opening base
- Brill poem about King and Queen visiting country
- Shooter overwhelms sober medical technician
- Where cones are located on street in front of van
- Trees take time to become predominant
Buddy explains!

The straight part
We know that "Earliest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case earliest = first.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 FIRST mean?
FIRST noun- The person or thing in the first position.
- The first gear of an engine.
- Something that has never happened before; a new occurrence.
- First base
- A first-class honours degree.
- A first-edition copy of some publication.
- A fraction of an integer ending in one.
- Preceding all others of a series or kind; the ordinal of one; earliest.
- Most eminent or exalted; most excellent; chief; highest.
- Before anything else; firstly.
- For the first time;
- Time; time granted; respite.