Shudder at having to compete with the awful child in it (7)
I believe the answer is:
vibrate
'shudder at' is the definition.
'vibrate' can be an answer for 'shudder' (thesaurus). I'm not certain of the 'at' bit.
'to compete with the awful child in it' is the wordplay.
'to compete with' becomes 'vie' (to vie with someone is to compete with them).
'the awful child' becomes 'brat' (brat is a kind of child. I am not sure about the 'awful' bit.).
'in it' means one lot of letters goes inside another.
'vie' enclosing 'brat' is 'VIBRATE'.
'having' is the link.
Can you help me to learn more?
(Other definitions for vibrate that I've seen before include "Oscillate rapidly" , "swing" , "tremble" , "Move rapidly to and fro" , "Shake, quiver, or throb" .)