Having the will to try tea out (7)
I believe the answer is:
testate
'having the will' is the definition.
(I've seen this before)
'try tea out' is the wordplay.
'try' becomes 'test' (synonyms).
'out' is an anagram indicator (out can mean wrong or inaccurate).
'tea' anagrammed gives 'ate'.
'test'+'ate'='TESTATE'
'to' acts as a link.
(Other definitions for testate that I've seen before include "Having left a legacy" , "State of having made a will" , "Having made a last will and testament" , "Having written a valid will" , "Leaving a will" .)