Lodgers essentially drink unlimited tea at the start, causing irritation (7)
I believe the answer is:
chagrin
'irritation' is the definition.
'lodgers essentially drink unlimited tea at the start' is the wordplay.
'essentially' means to look at the middle letters.
'unlimited' means to look at the middle letters (remove the limits/outer letters).
'tea' becomes 'cha' (cha is a type of tea).
'at the start' means one lot of letters go next to another.
The centre of 'lodgers' is 'g'.
The middle of 'drink' is 'rin'.
'g'+'rin'='grin'
'grin' put after 'cha' is 'CHAGRIN'.
'causing' acts as a link.
(Other definitions for chagrin that I've seen before include "irritation?" , "Arching with annoyed disappointment" , "Arching with annoyance and embarrassment" , "Feeling of annoyance and embarrassment" , "Disappointment, exasperation" .)