The most common and most likely answer to this crossword clue is the 10 plus 4 letter word CAPABILITY CAPA
C
A
P
A
B
I
L
I
T
Y
C
A
P
A
Buddy explains!
The straight part
We know that "competence" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case competence = capability capa.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.