Testing after one mile, and getting better (9)
I believe the answer is:
improving
'getting better' is the definition.
(I've seen this before)
'testing after one mile' is the wordplay.
'testing' becomes 'proving' ('prove' can be a synonym of 'test').
'after' means one lot of letters go next to another.
'one' becomes 'i' (Roman numeral).
'mile' becomes 'm' (common abbreviation).
'i'+'m'='im'
'proving' after 'im' is 'IMPROVING'.
'and' is the link.
(Other definitions for improving that I've seen before include "Recovering" , "Getting better" , "Making better" .)