Discovers a discoloration's covering half of saucer (10)
I believe the answer is:
ascertains
'discovers' is the definition.
(ascertaining is a kind of discovering)
'a discoloration's covering half of saucer' is the wordplay.
'discoloration's' becomes 'stain's' ('stain' can be a synonym of 'discoloration').
'covering' is an insertion indicator.
'half of' indicates taking half.
'saucer' cut in half is 'cer'.
'stains' placed around 'cer' is 'scertains'.
'a'+'scertains'='ASCERTAINS'
(Other definitions for ascertains that I've seen before include "Finds out" , "Discovers" .)