The most common and most likely answer to this crossword clue is the 6 letter word CADETS
C
A
D
E
T
S
Buddy explains!

The straight part
We know that "Colts accepting start of training" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case colts accepting start of training = cadets.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 CADETS mean?
CADETS noun- A student at a military school who is training to be an officer.
- A younger or youngest son, who would not inherit as a firstborn son would.
- (in compounds, chiefly in genealogy) Junior. (See also the heraldic term cadency.)
- A young man who makes a business of ruining girls to put them in brothels.
- A young gentleman learning sheep farming at a station; also, any young man attached to a sheep station.