Finally clean a dirty place that's vile (5)
I believe the answer is:
nasty
'vile' is the definition.
(synonyms)
'finally clean a dirty place' is the wordplay.
'finally' indicates one should take the final letters.
'dirty place' becomes 'sty' (as in a pig sty).
The last letter of 'clean' is 'n'.
'n'+'a'+'sty'='NASTY'
'that's' is the link.
(Other definitions for nasty that I've seen before include "grave" , "Evil" , "Highly repugnant" , "Filthy" , "Obscene" .)