The most common and most likely answer to this crossword clue is the 7 letter word CAT-SIT
C
A
T
-
S
I
T
Buddy explains!

The straight part
We know that "Perhaps to keep a Persian" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case perhaps to keep a persian = cat-sit.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 CAT-SIT mean?
CAT-SIT verb- To babysit for (take care of) a cat.