Little pest covers mad flier with a firearm (5,4,5)

'a firearm' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'little pest covers mad flier' is the wordplay.
I cannot really understand how this works, but
'little' could be 'small' (synonyms) and 'small' is found within the answer.
an anagram of 'flier' is 'erifl' which is located in the answer.
The remaining letters 'bore' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

'with' acts as a link.

Can you help me to learn more?