The president was irritated by being introduced to (9)
I believe the answer is:
presented
'the' is the definition.
I can't judge whether this defines the answer.
'president was irritated by being introduced to' is the wordplay.
I cannot really see how this works, but
'president' could be 'p' (common abbreviation eg in VP) and 'p' is located in the answer.
'being' could be 'ted' (Ted is an example) and 'ted' is located in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for presented that I've seen before include "Gave formally, award say" , "Introduced, brought forward" , "Made a gift to" , "Given" , "delivered pitch?" .)