Crossword Genius

Prime minister getting Speaker's cuppa (and what it soothes) (9)

Ross

I believe the answer is:

taoiseach

I'm a little stuck... Click here to teach me more about this clue!

'prime minister' is the definition.
(term for the Irish prime minister)

'speaker's cuppa and what it soothes' is the wordplay.
I cannot quite understand how this works, but
'speaker's' could be 'is' ('I' refers to the person saying it) and 'is' is found within the answer.
'cuppa' could be 't' and 't' is present in the answer.
'it' could be 'e' ('e' can mean 'electronic' which is similar to 'IT') and 'e' is found in the answer.
This explanation may well be incorrect...

'getting' acts as a link.

Can you help me to learn more?

(Other definitions for taoiseach that I've seen before include "Western PM" , "Irish head of government" , "I 'ate chaos (anag) - Irish Republic's prime minister" , "PM in Dublin" , "Irish premier" .)

I've seen this clue in The Telegraph.
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