Only 'seek' alone is correct if you are a careful user. 'Seek' means 'look for/after'.
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Resplenda. She was SOUGHT AFTER, and flattered.' then I guess the word ' after' here is only used to emphasize the fact that she was so wanted by men who had seen her ?I think that is a kind of idiom, 'to be sought after', Resplenda. In any case you will find other instances of seek for/after. It is common enough informally.
Resplenda Are there any differences between these two, if I may ask?I can think of none except the case you have already presented: 'Sought after' = highly desired.