Conrad worried another chap was strict (9)

I believe the answer is:

draconian

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'strict' is the definition.
(thesaurus)

'conrad worried another chap' is the wordplay.
'worried' indicates an anagram (worry can mean to interfere with or disturb).
'another chap' becomes 'ian' (man's name. I am not sure about the 'another' bit.).
'conrad' anagrammed gives 'dracon'.
'dracon'+'ian'='DRACONIAN'

'was' acts as a link.

Can you help me to learn more?

(Other definitions for draconian that I've seen before include "Savage" , "Cruel" , "Very harsh like severe laws" , "Excessively severe" , "Incan road (anag) - extremely harsh" .)

I've seen this clue in The Daily Express.

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