Cosmonaut, wildly enthusiastic, to call shortly (7)
I believe the answer is:
gagarin
'cosmonaut' is the definition.
(I've seen this before)
'wildly enthusiastic to call shortly' is the wordplay.
'wildly enthusiastic' becomes 'gaga' (I've seen this in another clue).
'to call' becomes 'ring' (telephone call).
'shortly' means to remove the last letter.
'ring' with its final letter taken off is 'rin'.
'gaga'+'rin'='GAGARIN'
(Other definitions for gagarin that I've seen before include "Yuri . . . . . . . made the first manned space flight" , "old spaceman" , "Yuri --, cosmonaut" , "circumnavigator" , "Yuri --, space pioneer" .)