A line cast out, or flung (5)

I believe the answer is:

shied

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'a line cast' is the definition.
'shied' can be an answer for 'cast' (I've seen this before). I am unsure of the 'a line' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for shied that I've seen before include "Thrown" , "Jumped nervously; threw" , "horse did this?" , "Cast" , "started" .)

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