Henry's letter to Mr Gore (3)
I believe the answer is:
hal
'henry's' is the definition.
(short for Henry)
'letter to mr gore' is the wordplay.
'letter' becomes 'h' ().
'to mr gore' becomes 'Al' (US politician Al Gore).
'h'+'al'='HAL'
(Other definitions for hal that I've seen before include "Odyssean character" , "Bluff Prince" , "Shakespeare's Prince_with Falstaff" , "future Henry V" , "Falstaff's prince (H.IV)" .)