Crew that's second-class getting teased (7)
I believe the answer is:
bragged
'crew' is the definition.
(I've seen this before)
'second-class getting teased' is the wordplay.
'second class' becomes 'b'.
'getting' is a charade indicator (letters next to each other).
'teased' becomes 'ragged' ('rag' can be a synonym of 'tease').
'b'+'ragged'='BRAGGED'
'that's' is the link.
(Other definitions for bragged that I've seen before include "Crew" , "Blew one's own trumpet" , "Boasted" .)