Every second counting, pair is doing something illegal (5)
I believe the answer is:
arson
'something illegal' is the definition.
(arson is a crime)
'every second counting pair is doing' is the wordplay.
'every second counting' indicates alternate letters.
'pair'+'is'+'doing'='pairisdoing'
The alternating letters of 'pairisdoing' are 'ARSON'.
(Other definitions for arson that I've seen before include "A burning crime" , "Malicious burning to destroy property" , "Crime of fire-setting (5)" , "Pyromaniac's crime" , "Malicious crime" .)