Dad turns up with his little pest! (5)
I believe the answer is:
aphis
'little pest' is the definition.
'aphis' can be an answer for 'pest' (I've seen this before). I am not sure about the 'little' bit.
'dad turns up with his' is the wordplay.
'dad' becomes 'pa' (both can mean one's father).
'turns up' shows that the letters should be reversed in order.
'with' is a charade indicator (letters next to each other).
'pa' backwards is 'ap'.
'ap'+'his'='APHIS'
Can you help me to learn more?
(Other definitions for aphis that I've seen before include "Sap-sucking garden pest" , "Greenfly" , "Small insect" , "sucker?" , "Plant louse" .)