Happen to give nothing cold to dog (5)
I believe the answer is:
occur
'happen' is the definition.
(I know that happen can be written as occur)
'give nothing cold to dog' is the wordplay.
'give' is a charade indicator (letters next to each other).
'nothing' becomes 'O' (O resembles 0).
'cold' becomes 'c' (eg on taps).
'to dog' becomes 'cur' (both can mean a despicable person).
'o'+'c' is 'oc'.
'oc'+'cur'='OCCUR'
'to' acts as a link.
(Other definitions for occur that I've seen before include "Turn up" , "appear" , "Go on" , "found" , "Befall" .)