The most common and most likely answer to this crossword clue is the 6 plus 9 letter word GOLDEN HANDSHAKE
I've seen this crossword clue in The Guardian
G
O
L
D
E
N
H
A
N
D
S
H
A
K
E
More clues leading to the result GOLDEN HANDSHAKE
- Midas-like grip necessary to get rid of employee?
- Ready for early retirement
- Very successful crew given fish as parting gift
- Improved P45 with information about former employees and fish
- Award one in Drake’s ship’s exchanged for a fish
- Ancient worker breaking into keg has drunk parting gift
- Midas touch gained at the end of career?
- Profitable redundancy has had dog-kennel converted
- After record’s brought up, office workers fish for pay-off
- Fair to offer jerk costly parting gift?
Buddy explains!

The straight part
We know that "to get rid of employee" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to get rid of employee = golden handshake.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.