Beginning to search Irish gentleman's address? (3)
I believe the answer is:
sir
'gentleman's address?' is the definition.
(I've seen this before)
'beginning to search irish' is the wordplay.
'beginning to' says to take the initial letters.
'irish' becomes 'IR' (abbreviation for Irish).
The first letter of 'search' is 's'.
's'+'ir'='SIR'
(Other definitions for sir that I've seen before include "as Winston Churchill was" , "Baronet's title" , "Feted fellow" , "Male form of address" , "Poet and novelist" .)