For the sake of a person’s mental health and well-being, everybody needs a someone to whom they can go about anything. Apart from friends and family, at work any teacher should have a line manager or other designated person.
In the UK our students, in their school lives, have their tutors or form teachers. The job of a tutor is fundamental to the well-being of the young people in their care. To have an adult who meets you every day, for however many minutes, and who has an overall view of how you are doing academically, socially and emotionally is an extraordinary privilege for our young people, who probably don't realise for the most part what benefit it can be to them.
Being a good tutor doesn't really have to demand a great deal of a teacher unless you have an overly prescribed and burdensome job description. Teachers probably report in their capacity as a tutor to a pastoral middle leader, maybe a Head of Section, Head of Year or Head of House. It would be wise for the relationship between the student and their tutor if this middle leader were to deal with any serious behavioural problems regarding a student. It would be sensible to keep this relationship as positive as possible, so that the student feels safe when communicating with the person they see at the start of every day.
As a tutor, your prime responsibility is not to take the register, hand out replacement timetables and chase up trip consent slips, however it may seem in those weekly weekly team briefings. Your responsibility as a Strictly Positive Tutor is first and foremost to create positive relationships with your students and be generally aware of what is going on in their lives. Your prime responsibility is to NOTICE. It should be a different relationship to that which students have with their other teachers. It should be ongoing, supportive, open and, insofar as is possible, non-judgemental. There are plenty of other adults who will judge anything a student does.
How much you feel confident to do as a tutor is something you need to consider ahead of taking up that responsibility. One thing you should remember is that the job of tutor is not one you applied for; it was allocated to you. Your pastoral line manager, however, probably did apply for that role. If you feel uncomfortable talking to a student about a particularly difficult or personal issue, or where you don't feel you can easily resolve a student's problem with another member of staff, or theirs with the student, don't be afraid to pass this on upwards with an explanation as to why you are doing so. That middle leader probably applied for that job in pastoral leadership as it takes them towards somewhere they want to go on their career trajectory. That brings with it responsibility.
Perhaps you might ask to attend the meeting, so that you can learn from witnessing and being part of the conversation, and that you can keep yourself involved. A conscientious middle leader will routinely invite the tutor to any meeting with the student and their parents or carers. You may want to consider in each case whether attendance at the meeting will improve or damage your relationship with the student - that should be the prime concern.
Like anything else, your skill as a tutor will grow over time, and with it your confidence. Naturally some teachers will embrace the pastoral side of the job, while others will find it toe-curling. I knew a very talented science teacher once, one of the most popular teachers in the school, a 'legend'. He absolutely hated one-to-one meetings with students who were upset or angry or otherwise emotional; he reported that he would freeze when he spotted tears gathering in a student's eye, or their face reddening with emotion. He did the bare minimum necessary before escalating it to the head of section. Other teachers are never happier than when handing over a cup of tea, leaning in to a meeting and trying to sort things out.
As I've said on practically every page of this book, it's up to you, within the framework of the school policies, how much you do before invoking higher authorities. The important thing is that you notice, that you show that you've noticed, and that the student knows that you are trying to do the best by them.