He is ejected from lively horse race that's increasingly rough (7)
I believe the answer is:
coarser
'he is ejected from lively horse race that's increasingly' is the definition.
The definition suggests a singular noun but the answer is not.
'rough' is the wordplay.
I cannot really understand how this works, but
'rough' could be 'coarse' (associated in meaning) and 'coarse' is found within the answer.
A single letter 'r' remains which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for coarser that I've seen before include "Comparatively crude" , "A scorer (anag.)" , "less refined" , "More vulgar" .)