Catches up with a chapter on American slave (9)

I believe the answer is:

spartacus

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'slave' is the definition.
(escaped slave)

'catches up with a chapter on american' is the wordplay.
'catches up with' becomes 'sparta' (I can't explain this - if you can you should give a lot more credence to this answer).
'a chapter' becomes 'c' (abbreviation).
'on' is a charade indicator (letters next to each other).
'american' becomes 'us' (abbreviation for United States).
'sparta'+'c'+'us'='SPARTACUS'

Can you help me to learn more?

(Other definitions for spartacus that I've seen before include "Roman slave leader - 1954 ballet composed by Aram Khachaturian - 1960 film starring Kirk Douglas" , "Roman revolutionary" , "Rebellious Roman slave. d. c.71BC" , "Rebel Roman slave" , "Roman slave who led an uprising against Roman legions" .)

I've seen this clue in The Telegraph.

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