Lady Caroline beginning to draft a letter (6)
I believe the answer is:
lambda
'letter' is the definition.
(lambda is a kind of letter of the alphabet)
'lady caroline beginning to draft a' is the wordplay.
'lady caroline' becomes 'Lamb' (19th-century novelist Lady Caroline Lamb).
'beginning to' suggests taking the first letters.
The initial letter of 'draft' is 'd'.
'lamb'+'d'+'a'='LAMBDA'
(Other definitions for lambda that I've seen before include "Greek letter - am bald (anag)" , "Teasing entertainer" , "Eleventh Greek letter" , "The 11th letter of the Greek alphabet" , "Foreign character" .)