For a bit of fun, start singing in plane (4)
I believe the answer is:
jest
'for a bit' is the definition.
(thesaurus)
'start singing in plane' is the wordplay.
'start' suggests taking the first letters.
'in' is an insertion indicator.
'plane' becomes 'jet' (jet plane).
The initial letter of 'singing' is 's'.
's' put into 'jet' is 'JEST'.
'of fun' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for jest that I've seen before include "Sally" , "In ____, playfully" , "` `Many a true word is spoken in . . . .' '" , "Ridicule" , "Humorous remark" .)