Match official in tie finally to improve (6)
I believe the answer is:
refine
'improve' is the definition.
(I know that refine is a more specific form of the action distill)
'match official in tie finally' is the wordplay.
'match official' becomes 'ref' (short for referee).
'finally' says to take the final letters.
The last letter of 'tie' is 'e'.
'ref'+'in'+'e'='REFINE'
'to' acts as a link.
(Other definitions for refine that I've seen before include "Remove impurities or make cultured" , "Cleanse from impurities" , "Purify or improve" , "Filter or process as with oil" , "Get rid of impurities" .)