Signify assent about English branch, saying nothing about independent element (9)
I believe the answer is:
neodymium
'element' is the definition.
(neodymium is a kind of element)
'signify assent about english branch saying nothing about independent' is the wordplay.
I cannot really understand how this works, but
'english' could be 'e' (abbreviation) and 'e' is located in the answer.
'assent' could be 'nod' and 'nod' is found within the remaining letters.
'independent' could be 'i' and 'i' is located in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Another definition for neodymium that I've seen is " toxic element".)