By being desperate at heart (3)
I believe the answer is:
per
'by' is the definition.
(I've seen this in another clue)
'desperate at heart' is the wordplay.
'at heart' says the answer is hidden in the clue (letters hidden in the heart of the clue).
'PER' can be found hidden inside 'desperate'.
'being' acts as a link.
(Other definitions for per that I've seen before include "According to" , "Preposition indicating by means of" , "For each or every" , "Preposition meaning for each" .)