Get cross having to rush away before the opener (3,3,3,6)

'get cross' is the definition.
(to fly off the handle is to become angry suddenly)

'to rush away before the opener' is the wordplay.
I cannot quite understand how this works, but
'rush' could be 'fly' (both can mean to hurry) and 'fly' is located in the answer.
'away' could be 'off' (synonyms) and 'off' is found within the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found within the answer.
'opener' could be 'handle' (something which opens, eg a door handle) and 'handle' is found within the answer.
The remaining letters 'he' is a valid word which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).

'having' acts as a link.