Northern man after turning up at function (7)
I believe the answer is:
tangent
'function' is the definition.
(tangent is a kind of function)
'northern man after turning up at' is the wordplay.
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'man' becomes 'gent' (gent is a kind of man).
'after' is a charade indicator (letters next to each other).
'turning up' shows that the letters should be reversed in order.
'at' back-to-front is 'ta'.
'n'+'gent'='ngent'
'ngent' after 'ta' is 'TANGENT'.
(Other definitions for tangent that I've seen before include "Straight line resting on a circle" , "A new line of thought" , "Line grazing another" , "mostly irrelevant item" , "line in mathematics" .)