It takes only a trice to complete her name! (3)

I believe the answer is:

bea

I'm a little stuck... Click here to teach me more about this clue!

'her name' is the definition.

'it takes only a trice to complete' is the wordplay.
I cannot quite see how this works, but
'it' could be 'e' ('e' can mean 'electronic' which is similar to 'IT') and 'e' is found in the answer.
'a' is within the answer.
A single letter 'b' remains which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

I've seen this clue in the Evening Standard.

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