... naughty sweetheart is desired (4)
I believe the answer is:
bade
'is desired' is the definition.
(past tense of bid, as in to command or require)
'naughty sweetheart' is the wordplay.
'naughty' becomes 'bad' (similar in meaning).
'sweetheart' becomes 'e' (the heart/centre of 'sweet').
'bad'+'e'='BADE'
(Other definitions for bade that I've seen before include "Ordered" , "Commanded with bead" , "Invited" .)