My son is Year 3, we live overseas at the moment and were supposed to be relocating to the UK in June but are left here in limbo at the moment. I homeschool my eldest and have been homeschooling my son since March when the schools closed. For this reason, I have experience of home education but also, I'm in the tricky situation where I have no school support and have to organise my Year 3's education. If you can only afford one session a week of tutoring, I would scrap this idea and have a look into some online learning programmes. You pay for them but much less than a tutor.
Conquer Maths - This is a brilliant online Maths tutor. There are recorded lessons followed by online questions. It is all set up by Year level inline with the curriculum and it is outstanding. My son does 4 lessons one here talking him about 30 minutes plus there are times tables games. This is brilliant, you pay for a Years Subs so it would be good as a topup once your son goes back to school.
For Literacy, Edplace and Literacy planet is useful.
On Facebook, look up E-Learning with Amy. She is a brilliant young tutor who regularly does curriculum-aligned soon tutoring in small groups. My eldest just did a 6 week long KS3 Transaction writing course. She sets assignments (parents to mark) but the cost is only £18 for the 6 weeks. She does KS2 courses also. If you don't want to do them live she sends the recordings.
For Science, I recommend KS2 Science courses with Graham Bray, a retired Science teacher. It costs £59.99 for a lifetime subscription. He narrates Science presentations and provides worksheets and they also work alongside the CGP Science books. It is very good.
Other things that he can do when you are working. Get a list of Year 4 recommended reading lists. Get him doing 30 minutes of silent reading daily. If you want him to have a go at higher level books, maybe buy the audible version and let him follow it with a paper version.
Does he have a tablet? Spellings apps like Squeebles Spellings and Timetables are excellent. My son does 15 minutes of each daily. No input from me needed. I think most teachers would be happy if all primary school children went back with quick recall of times tables
Can he tell the time easily? If not make sure he is doing 15 minutes of a Telling the time app until he nails it.
A decent tutor would probably cost around £30 a week for one hour. I think you would be better off exploring other online learning options that are out there like subs which will also keep you covered if there are interruptions to school later on in the year. As long as your son has access to a tablet or PC then there are lots of options that can help him without a tutor.