Slowing down in the end, curiously engrossed (10)
I believe the answer is:
enthralled
'engrossed' is the definition.
(engrossed can mean enthralled or captivated)
'slowing down in the end curiously' is the wordplay.
'slowing down' becomes 'rall' (short for rallentando, musical term).
'in' indicates putting letters inside.
'curiously' indicates anagramming the letters.
'the'+'end'='theend'
'theend' anagrammed gives 'enthed'.
'rall' placed inside 'enthed' is 'ENTHRALLED'.
(Other definitions for enthralled that I've seen before include "Spellbound" , "Captivated" .)