Drink that is covering minute part of apron (6)
I believe the answer is:
imbibe
'drink' is the definition.
(I know that drink can be written as imbibe)
'that is covering minute part of apron' is the wordplay.
'that is' becomes 'ie' (abbreviation for id est, 'that is' in Latin).
'covering' means one lot of letters goes inside another.
'minute' becomes 'm' (abbreviation).
'part of apron' becomes 'bib' ('bib' is part of 'apron').
'm'+'bib'='mbib'
'ie' going around 'mbib' is 'IMBIBE'.
(Other definitions for imbibe that I've seen before include "Drink in - assimilate" , "Tope" , "Swallow" , "Drink (alcohol)" , "Take in (with one's mother's milk?)" .)