Dear Dave, 
Hope this email finds you well. 
I’m looking for a coach to teach chess for my 7-year-old daughter. 
My friend recommended you, but I don’t know whether you are available or have available space for a beginner. 
Look forward to your reply.

Thanks for your interest.

I am available for coaching and have space, but I would not like to charge you money to teach a beginner.

Beginners mostly need practice, and some basic advice which is freely available.

If she has no opponents at home or at school, then I suggest you sign her up at ChessKid.com (a child-friendly place to play) or at lichess.org (an adult space, but you can turn off chat, so you can only say things to each other like ‘Good game’ and ‘Thank you’).  You can also get computer and ‘phone apps which play chess:
https://www.dadsuggests.com/home/best-chess-apps
The free level of ‘Play Magnus’ might amuse.  Some of the free chess apps like Stockfish are of Grandmaster strength, so watch out for that!

Beginners nearly always lose (or win) games because they miss (or spot) captures and simple tactics.
There are places where you can practise simple tactics for free, including lichess.org.
https://lichess.org/training
To learn what the simple tactics patterns are, you can refer to
https://devonjuniorchess.co.uk/content/middlegame-tactics-advice
https://devonjuniorchess.co.uk/content/course-chess-tactics
Someone made a video series out of that last collection:

And for defending:

Playing games and revising simple tactics are the most important things to start with.

She will also need to know how to finish off a game of chess:

And to start a game properly:
https://devonjuniorchess.co.uk/content/openings-advice

For more basic advice, try these resources:

https://www.chessinschools.co.uk/chess-at-home

and if modesty permits:
https://onionschess.co.uk/content/4-book-deal

If she does not like to read books, there are many videos on YouTube which are free.  I have made some myself, as you see.

I hope some of that is helpful.

For coaching, I charge £30 per hour, and for a month’s worth of lessons, I expect you can buy all the books your daughter might need for her first year or two of playing chess!

If she starts to play on lichess.org, let me know what her online name is (I am drdaveexeter), and I will be able to see her games, and I can tell you which bits of advice need more attention.