Reason to admit letterhead was part of the contract (6)
I believe the answer is:
clause
'part of the contract' is the definition.
(I've seen this before)
'reason to admit letterhead' is the wordplay.
'reason' becomes 'cause' (I've seen this before).
'to admit' indicates putting letters inside.
'letterhead' becomes 'l' (head letter of 'letter').
'cause' going around 'l' is 'CLAUSE'.
'was' is the link.
(Other definitions for clause that I've seen before include "Separate item in contract" , "Joker, say" , "Subunit of a sentence" , "Verb-carrying component of sentence" , "Subordinate part of sentence" .)