Relationships: my seven-year-old daughter refuses to talk at school
Our family moved to Hong Kong this summer from Italy. We used to live in a small town, with extended family nearby. I have three girls aged five, seven and 11. My elder and younger have settled well, but my middle child simply refuses to talk in school.

It is frustrating and worrying to see your child suffer in school and not able to settle down, like your other two daughters.
From what you describe, it seems your daughter is able to talk, which indicates it might not be an organic problem that affects her speech.
Focus less on the problem and you will see other aspects of your daughter thriving
I could not give you a diagnosis here, but it does sound like her situation matches closely some of the diagnostic criteria for selective mutism (SM). Some of the main hallmarks of SM are social anxiety, oppositional behaviour and communication problems.
According to the American Psychiatric Association, a key diagnostic feature of the condition is "persistent failure to speak in specific social situations where speech is expected, despite speaking in other situations".
However, if you want a diagnosis, it is best to have her seen by a speech-language pathologist, in addition to a paediatrician and a psychologist or psychiatrist. You should aim to work with them as a team and to develop an intervention plan. Shyness, bilingualism and her age group (four to eight) are some of the predisposing factors of SM. It is often triggered by relocation, especially to a place where the child needs to adapt to another language and culture.
SM is often caused by social anxiety, therefore affected children tend to respond well to a short course of behaviour therapy or exposure-based therapy.
Home-based therapy also helps build your child's confidence without causing additional anxiety. Once trust has been built, the therapy session can move to the school, which usually helps strengthen the child's confidence there, too.