Character in chase caught with no shoes finally (5)
I believe the answer is:
ethos
'character' is the definition.
(moral character)
'chase caught with no shoes finally' is the wordplay.
'finally' suggests the final letters.
The last letters of 'chase caught with no shoes' are 'ETHOS'.
'in' is the link.
(Other definitions for ethos that I've seen before include "Those with characteristic beliefs or spirit" , "moral code" , "Moral character" , "Spirit (of, eg, an age)" , "Moral atmosphere" .)