I assume that you won't have a Bristol address until well past the normal application deadline for secondary schools, which I think is some time this autumn?
In which case I agree that if you're not moving until the summer and want a yr7 place for September, you're highly unlikely to get one at Cotham, Redland Green or Bristol Cathedral (which are the three closest state schools to Clifton & Redland), as they are always heavily oversubscribed. Only chance would be to move right next door to one or other of the schools so that you are top of the waiting list for the first place that comes up. And that wouldn't work for the cathedral school as it doesn't go on distance.
You don't mention being religious - there are a couple of good Catholic secondaries and one CofE, where baptism/attendance records could help you get a place, but again those schools are popular and oversubscribed, so you'd just be hoping to be near the top of the waiting list.
Otherwise you will probably be allocated a place at one of the least popular schools several miles away - and although they have been improving, a large number of Bristol secondary schools don't have a great reputation for academic results, behaviour etc.
Private schools would be a more reliable option, but for BGS or QEH you'd need to start the application process this autumn and get your DS to take the entrance tests for one or both in January, as they also have more than enough applicants to fill their places most years - it's got harder to get in at year 7 for both of them recently because they have expanded their junior schools, so more children are coming up from within the school.
Clifton College is on the traditional prep/senior school model, so the main intake is at ages 7 and 13 (year 9), though they always get a few joining at year 7. I'm not sure about entrance test dates. There is also Clifton High School, which was girls-only and is now mixed, though boys are still heavily outnumbered, which may put you off. Academic reputation is also considerably below QEH, BGS etc.
State primary places can also be hard to find, but there are more primary schools in the area. Clifton has St John's, Christ Church and Hotwells, Redland has Colston's primary (not to be confused with Colston's girls, which is a secondary academy, or Colston's School, which is a mixed private school), or Westbury Park (near the top end of Redland, and the local primary for a chunk of the Redland Green catchment area). You stand a reasonable chance of a year 5 place coming up at one or other of those schools because these areas have quite a mobile population, and also a number of children move from the state to the private sector in years 5 and 6. But it all depends on being in the right place on the waiting list at the right time when a place comes up.
All the private schools have junior schools as well.