Beseech space visitor to produce (5)
I believe the answer is:
beget
'to produce' is the definition.
(I've seen this in another clue)
'beseech space visitor' is the wordplay.
'beseech' becomes 'beg' (I've seen this before).
'space visitor' becomes 'et' (I can't explain this - if you can you should give a lot more credence to this answer).
'beg'+'et'='BEGET'
Can you help me to learn more?
(Other definitions for beget that I've seen before include "Father" , "Produce (child) (archaic)" , "Sire" , "Bring about, cause" , "Give rise to; create (children)" .)