Thief beats up beloved in Paris (8)
I believe the answer is:
snatcher
'thief' is the definition.
(snatcher is a kind of thief)
'beats up beloved in paris' is the wordplay.
'beats' becomes 'tans' (tan can mean to beat or hit).
'up' is a reversal indicator (in down clue: letters go upwards).
'beloved in paris' becomes 'cher' ('dear' or 'beloved' in French).
'tans' written backwards gives 'snat'.
'snat'+'cher'='SNATCHER'
(Other definitions for snatcher that I've seen before include "Thief" , "Stealer; kidnapper" , "See 1" , "Person grabbing" , "One seizing suddenly" .)