Hope and Crosby going up and down (7)
I believe the answer is:
bobbing
'going up and down' is the definition.
(I've seen this before)
'hope and crosby' is the wordplay.
'hope' becomes 'bob' (comedian Bob Hope).
'and' means one lot of letters go next to another.
'crosby' becomes 'bing' (singer Bing Crosby).
'bob'+'bing'='BOBBING'
(Other definitions for bobbing that I've seen before include "Curtseying; cutting (hair) short" , "jumping up and down" , "going up and down" , "taking a quick bow" .)