Jack and Nigel arranged short catchy tune (6)

I believe the answer is:

jingle

I'm a little stuck... Click here to teach me more about this clue!

'catchy tune' is the definition.
(I've seen this before)

'jack and nigel arranged' is the wordplay.
'jack' becomes 'J' (playing card abbreviation).
'and' says to put letters next to each other.
'arranged' indicates an anagram (letters rearranged).
'nigel' is an anagram of 'ingle'.
'j'+'ingle'='JINGLE'

'short' is the link.
I am not very happy about this link. It may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for jingle that I've seen before include "Catchy rhyme" , "Tune for TV commercial" , "Metallic sound as of coins in pocket" , "imposed on Pickwick Club" , "Catchy song" .)

I've seen this clue in The Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.