The most common and most likely answer to this crossword clue is the 10 letter word PRIORITISE
I've seen this crossword clue in The Daily Telegraph
P
R
I
O
R
I
T
I
S
E
More clues leading to the result PRIORITISE
Buddy explains!

The straight part
We know that "Make first" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make first = prioritise.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 PRIORITISE mean?
PRIORITISE verb- To arrange or list a group of things in order of priority or importance.
- To rank something as having high priority.