Quiet husband holding European record is shamefaced (8)
I believe the answer is:
sheepish
'shamefaced' is the definition.
(I've seen this before)
'quiet husband holding european record is' is the wordplay.
'quiet' becomes 'sh' (**).
'husband' becomes 'h'.
'holding' indicates putting letters inside.
'european' becomes 'e' (abbreviation e.g. EU).
'record' becomes 'ep'.
'sh'+'h'='shh'
'e'+'ep'+'is'='eepis'
'shh' enclosing 'eepis' is 'SHEEPISH'.
(Other definitions for sheepish that I've seen before include "Shy, shamefaced" , "describing 3 [ROMNEY] ?" , "Embarrassed, looking silly" , "Shy, embarrassed" , "embarrassment" .)