Quiet European married Arkwright’s son (4)
I believe the answer is:
shem
'son' is the definition.
(I have seen 'Son of Noah ' mean 'shem' so perhaps 'son' could also mean 'shem')
'quiet european married' is the wordplay.
'quiet' becomes 'sh' (both can be said to tell someone to be quiet).
'european' becomes 'E' (abbreviation e.g. EU).
'married' becomes 'm' (abbreviation, e.g. in genealogy).
'sh'+'e'+'m'='SHEM'
'arkwright's' is the link.
This may not be correct. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for shem that I've seen before include "Biblical character" , "Noah's son caught in mess" , "Eldest of Noah's three sons" , "Noah's eldest son" , "One of Noah's sons" .)