Lily heading off from old rotten borough (4)
I believe the answer is:
arum
'lily' is the definition.
(a type of lily)
'heading off from old rotten borough' is the wordplay.
'heading off from' means to remove the first letter.
'old rotten borough' becomes 'Sarum' (as in Old Sarum - former parliamentary constituenc).
'sarum' with its initial letter removed is 'ARUM'.
(Other definitions for arum that I've seen before include "Plant like cuckoo pint" , "Plant with small flowers and arrow-shaped leaves - kind of lily" , "Eg, cuckoo pint" , "Cuckoo pint genus" , "Type of 1 Across" .)