Heartless Beatle describing McCartney's first as dud (5)
I believe the answer is:
lemon
'dud' is the definition.
(I've seen this in another clue)
'heartless beatle describing mccartney's first' is the wordplay.
'heartless' means to remove the middle letters.
'beatle' becomes 'lennon' (John Lennon).
'describing' means one lot of letters goes inside another (describe can mean to form the outline of).
'mccartney's first' becomes 'm' (1st letter of 'mccartney').
'lennon' with its middle removed is 'leon'.
'leon' placed around 'm' is 'LEMON'.
'as' acts as a link.
(Other definitions for lemon that I've seen before include "Tone" , "Defective object" , "Pale yellow, as of citrus fruit" , "Small evergreen fruit tree" , "Melon is another fruit" .)