Believe what could be a sign of summer coming? (7)
I believe the answer is:
swallow
I believe this clue is a double definition.
'believe' is the first definition.
(swallowing is a kind of believing)
'what could be a sign of summer coming?' is the second definition.
(migrating swallows are a sign of summer)
(Other definitions for swallow that I've seen before include "Long-winged, fork-trailed bird" , "Songbird" , "One of these does not make a spring" , "Take in - migratory bird" , "Bird - gulp down" .)