Will try to accept pet name (9)
I believe the answer is:
testament
'will' is the definition.
(synonyms)
'try to accept pet name' is the wordplay.
I cannot quite see how this works, but
'try' could be 'test' (test is a kind of try) and 'test' is found within the answer.
an anagram of 'name' is 'amen' which is located in the answer.
A single letter 't' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for testament that I've seen before include "Tribute" , "Either of the two main divisions of the Bible" , "(Person's) will" , "Will - part of bible" , "evidence" .)