Last of precious metal covering European beer mug (5)
I believe the answer is:
stein
'beer mug' is the definition.
('stein' can be a synonym of 'beer mug')
'last of precious metal covering european' is the wordplay.
'last of' suggests the final letters.
'metal' becomes 'tin' (tin is a kind of metal**).
'covering' means one lot of letters goes inside another.
'european' becomes 'e' (abbreviation e.g. EU).
The last letter of 'precious' is 's'.
'tin' going around 'e' is 'tein'.
's'+'tein'='STEIN'
(Other definitions for stein that I've seen before include "Glass" , "Inset (anag.)" , "German tankard" , "Beer-mug" , "Earthenware beer jug" .)