Propose unusual Irish name in letter (8)
I believe the answer is:
nominate
'propose' is the definition.
(synonyms)
'unusual irish name in letter' is the wordplay.
'unusual irish name' becomes 'mina' (I am not sure about this - if you are sure you should believe this answer much more).
'in' is an insertion indicator.
'letter' becomes 'note' (note is a kind of letter).
'mina' put inside 'note' is 'NOMINATE'.
Can you help me to learn more?
(Other definitions for nominate that I've seen before include "Designate" , "Specify (person for job)" , "Propose as a candidate" , "Put forward name for a mention" , "Propose - a mention (anag)" .)