Irritating leader leaving town, having snatched children (5)
I believe the answer is:
itchy
'irritating' is the definition.
(an itch is irritating)
'leader leaving town having snatched children' is the wordplay.
'leader leaving' means to remove the first letter.
'town' becomes 'city' (city is a type of town).
'having snatched' is an insertion indicator.
'children' becomes 'ch' (genealogical abbreviation).
'city' with its first letter taken off is 'ity'.
'ity' enclosing 'ch' is 'ITCHY'.
(Other definitions for itchy that I've seen before include "Tingling - desirous" , "Making one want to scratch" , "Fidgety" , "Feeling as if one wants to scratch" , "Irritating to the skin" .)