This person has alien encounter (4)
I believe the answer is:
meet
'encounter' is the definition.
(I know that encounter can be written as meet)
'this person has alien' is the wordplay.
'this person' becomes 'me' (the person writing).
'has' means one lot of letters go next to another.
'alien' becomes 'et' (extra terrestrial).
'me'+'et'='MEET'
(Other definitions for meet that I've seen before include "See 24" , "sporting occasion" , "Attend" , "Fitting to come together" , "Happen upon" .)