Pressure to encourage expulsion (5)
I believe the answer is:
purge
'expulsion' is the definition.
(an expulsion is a purge or removal)
'pressure to encourage' is the wordplay.
'pressure' becomes 'p' (abbreviation).
'to encourage' becomes 'urge' (I've seen this before).
'p'+'urge'='PURGE'
(Other definitions for purge that I've seen before include "Exterminate" , "elimination of opponents" , "pogrom" , "Purify, clear out" , "Remove undesirable elements" .)