I start to raise it in allotment, producing annoyance (10)

'annoyance' is the definition.
(I know that annoyance can be written as irritation)

'i start to raise it in allotment' is the wordplay.
'start to' suggests taking the first letters.
'in' means one lot of letters goes inside another.
'allotment' becomes 'ration' (I've seen this in another clue).
The initial letter of 'raise' is 'r'.
'it' inserted within 'ration' is 'ritation'.
'i'+'r'+'ritation'='IRRITATION'

'producing' acts as a link.