Nasty kid runs into club (4)
I believe the answer is:
brat
'nasty kid' is the definition.
(I've seen this in another clue)
'runs into club' is the wordplay.
'runs' becomes 'r' (cricket abbreviation).
'into' is an insertion indicator.
'club' becomes 'bat' (as in sporting equipment).
'r' put inside 'bat' is 'BRAT'.
(Other definitions for brat that I've seen before include "Horrible child" , "An obnoxious or spoiled child" , "Mervyn -- (Titus Groan)" , "annoying young fellow" , "Very dry" .)