Cancelled by Henry, with or without consideration (7)
I believe the answer is:
offhand
'without consideration' is the definition.
(I've seen this before)
'cancelled by henry with' is the wordplay.
'cancelled' becomes 'off' ('off' can be similar in meaning to 'cancelled').
'by' means one lot of letters go next to another.
'henry' becomes 'h' ('H' can be a synonym of 'henry').
'with' becomes 'and' (I've seen this before**).
'off'+'h'+'and'='OFFHAND'
'or' acts as a link.
(Other definitions for offhand that I've seen before include "Casually rude" , "Ungraciously curt" , "Ungraciously cool" , "Ad lib" , "Rudely casual; impromptu" .)