Paint executive assistant astride horse, having tantrum? (3,7)

'paint executive assistant astride' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'horse having tantrum?' is the wordplay.
I cannot quite understand how this works, but
'horse' could be 'gg' (geegee or GG is a childish term for a horse) and 'gg' is found in the answer.
'tantrum?' could be 'temper' (I've seen this before) and 'temper' is located in the answer.
The remaining letters 'ea' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?