Pigheadedly press for removal of undesirables (5)
I believe the answer is:
purge
'removal of undesirables' is the definition.
'purge' can be an answer for 'removal' (thesaurus). I am not certain of the 'of undesirables' bit.
'pigheadedly press for' is the wordplay.
'pigheadedly' becomes 'p' (this could be a standard abbreviation which I don't know about).
'press for' becomes 'urge' (I've seen this in another clue).
'p'+'urge'='PURGE'
Can you help me to learn more?
(Other definitions for purge that I've seen before include "Cleanse, purify" , "empty bowels" , "Elimination of "undesirables"" , "Eliminate or expiate" , "Violent expulsion" .)