Endlessly irritable educationist means to create experimental environment (4,3)
I believe the answer is:
test bed
'experimental environment' is the definition.
(environment where tests or experiments can be done)
'endlessly irritable educationist' is the wordplay.
'endlessly' means to remove the last letter.
'irritable' becomes 'testy' (testy can mean irritable or annoyed).
'educationist' becomes 'bed' (educational qualification).
'testy' with its last letter taken away is 'test'.
'test'+'bed'='TEST-BED'
'means to create' is the link.
(Other definitions for test bed that I've seen before include "place for experimental trials" , "engineers are working on it" , "Practise sleeping" , "trial equipment" .)