The most common and most likely answer to this crossword clue is the 6 plus 1 plus 6 letter word BACKED A WINNER
I've seen this crossword clue in The Daily Telegraph
B
A
C
K
E
D
A
W
I
N
N
E
R
Buddy explains!
The straight part
We know that "Got a first of course" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case got a first of course = backed a winner.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.