Handled Irish politician keeping engineers worried (7)
I believe the answer is:
treated
'handled' is the definition.
('treat' can be a synonym of 'handle')
'irish politician keeping engineers worried' is the wordplay.
'irish politician' becomes 'td' (Teachta Dala, meaning an Irish parliament member).
'keeping' means one lot of letters goes inside another.
'engineers' becomes 're' (Royal Engineers).
'worried' becomes 'ate' (I've seen this before).
're'+'ate'='reate'
'td' going around 'reate' is 'TREATED'.
(Other definitions for treated that I've seen before include "Applied medication to" , "not asked to pay" , "Dealt with" , "Given medical attention" , "taken out" .)