Cause embarrassment to a party (5)
I believe the answer is:
abash
'cause embarrassment' is the definition.
(to abash someone is to make them embarrassed)
'a party' is the wordplay.
'party' becomes 'bash' (term for a party or celebration).
'a'+'bash'='ABASH'
'to' is the link.
(Other definitions for abash that I've seen before include "Cause to feel 4" , "Bring shame on" , "Cause embarrassment" , "Cause to feel ashamed" , "show up" .)