The most common and most likely answer to this crossword clue is the 4 plus 3 plus 3 letter word OVER THE BAR
I've seen this crossword clue in The Guardian
O
V
E
R
T
H
E
B
A
R
Buddy explains!

The straight part
We know that "Landlord’s position/where conversion is successful" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case landlord’s position/where conversion is successful = over the bar.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.