Sudden entrance caused by his getting run out (6)
I believe the answer is:
inrush
'sudden entrance' is the definition.
'inrush' can be an answer for 'entrance' (I have seen 'hasty entrance' mean 'inrush' so perhaps 'entrance' could also mean 'inrush'). I'm unsure of the 'sudden' bit.
'his getting run out' is the wordplay.
'getting' says to put letters next to each other.
'out' indicates an anagram (out can mean wrong or inaccurate).
'his' after 'run' is 'runhis'.
'runhis' is an anagram of 'INRUSH'.
'caused by' is the link.
Can you help me to learn more?
(Other definitions for inrush that I've seen before include "Sudden arrival or entry" , "quick entry" , "gaining sudden entry" , "Sudden surge" , "Sudden move inwards" .)