Nelson and Hardy's first speech unfinished (7)
I believe the answer is:
horatio
'nelson' is the definition.
(I've seen this before)
'hardy's first speech unfinished' is the wordplay.
'first' suggests taking the first letters.
'speech' becomes 'oration' (oration is a kind of speech).
'unfinished' means to remove the last letter.
The initial letter of 'hardys' is 'h'.
'oration' with its final letter removed is 'oratio'.
'h'+'oratio'='HORATIO'
'and' acts as a link.
(Other definitions for horatio that I've seen before include "Nelson's first name" , "Nelson's given name" , "Good seafaring name" , "part of Hamlet" , "Speaker of Good night, sweet prince (Hamlet)" .)