Choose out-of-this-world person to encourage workers to strike (6)
I believe the answer is:
picket
'encourage workers to strike' is the definition.
(as in a picket line on a strike)
'choose out-of-this-world person' is the wordplay.
'choose' becomes 'pick' (picking is a kind of choosing).
'out-of-this-world person' becomes 'ET' (alien in the film ET).
'pick'+'et'='PICKET'
'to' acts as a link.
(Other definitions for picket that I've seen before include "Group of striking workers outside workplace" , "Type of wooden fence" , "Trade union protestor(s) outside a place of work" , "Wooden stake for a fence" , "Line of workers on strike duty" .)