Dear mistress's last minute relationship (7)
I believe the answer is:
sweetie
'dear' is the definition.
(both are terms of endearment)
'mistress's last minute relationship' is the wordplay.
'last' indicates one should take the final letters.
'minute' becomes 'wee' (I've seen this before).
'relationship' becomes 'tie' (tie is a kind of relationship).
The last letter of 'mistresss' is 's'.
's'+'wee'+'tie'='SWEETIE'
(Other definitions for sweetie that I've seen before include "dear" , "Darling" , "Love" , "Barley sugar, for example" , "Term of endearment" .)