Linked with an out-of-line Edwardian (4)
I believe the answer is:
tied
'linked' is the definition.
(tying is a kind of linking)
'line edwardian' is the wordplay.
'line' becomes 'tie' (tie is a kind of line).
'edwardian' becomes 'd' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'tie'+'d'='TIED'
'with an out-of' acts as a link.
This may not be correct. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for tied that I've seen before include "Fastened with string" , "Made into a knot" , "Made bow" , "Drawn" , "Restricted, bound" .)