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