Native blue dye — American, without English name (10)
I believe the answer is:
indigenous
'native' is the definition.
(similar in meaning)
'blue dye american without english name' is the wordplay.
'blue dye' becomes 'indigo' (I've seen this in another clue).
'american' becomes 'US' (abbreviation for United States).
'without' indicates putting letters inside ('without' can be similar in meaning to 'outside').
'english' becomes 'E' (abbreviation as in OED).
'name' becomes 'n' (common abbreviation e.g. on forms).
'indigo'+'us'='indigous'
'e'+'n'='en'
'indigous' going around 'en' is 'INDIGENOUS'.
(Another definition for indigenous that I've seen is " Native".)