Bond chasing criminal with European in formal evening dress (5,3)
I believe the answer is:
white tie
'formal evening dress' is the definition.
(I've seen this before)
'bond chasing criminal with european' is the wordplay.
'bond' becomes 'tie' (both can mean a connection).
'chasing' means one lot of letters go next to another (some letters chase after others).
'criminal' indicates anagramming the letters.
'european' becomes 'e' (abbreviation e.g. EU).
'with' with letters rearranged gives 'whit'.
'whit'+'e'='white'
'tie' put after 'white' is 'WHITE-TIE'.
'in' acts as a link.
(Other definitions for white tie that I've seen before include "formal item" , "formal evening dress" , "Like formal do" , "posh occasion?" , "Formal dress code" .)