Henry left Theresa outside - that's not appreciated (9)
I believe the answer is:
'not appreciated' is the definition.
'henry left theresa outside' is the wordplay.
'henry' becomes 'hank'.
'left' becomes 'l' (common abbreviation).
'theresa' becomes 'tess'.
'outside' is an insertion indicator.
'hankl' going inside 'tess' is 'THANKLESS'.
'that's' is the link.
(Other definitions for thankless that I've seen before include "Receiving no appreciation" , "Showing no gratitude" , "Unappreciated" .)