Hedge/Tree for privacy

Hello. Newbie here

I'm looking for recommendations on a quick growing hedge or tree for privacy.

The situation is we have a nightmare neighbour. We're hoping she's going to be moved on soon, but for now we need a little bit of extra privacy when we sit in our garden of an evening. We've ordered a fake ivy covered trellis which we're going to place the right of our front door....between our garden and hers. This will be 3 foot wide and will give us some privacy.

Our garden starts right after that so we also want to plant something which will grow (quickly) to around 6 foot, with a decent spread, which will give us a little bit more privacy next to the trellis. We want this to be freestanding, i.e. so it doesn't need a fence or trellis to reach it's height.

I hope that all makes sense Any recommendations welcome.

Depends on how soon she may be moved on, if at all.

Most things that grow quickly need support by means of trellis's or fences. Things like Clematis, Honeysuckle etc can grow quite rapidly if you get the correct variety but the do need supporting.

If it's short term, maybe think about annual plants, though it is a little late in the year - climbing nasturtiums, runner beans, Jerusalem artichokes, things like that.
Beyond that - as Conny suggests - fast perennial climbers on a simple trellis, I'd include a few fruiting plants as possibilities - Japanese Wineberry, thornless blackberry, grapevine.
You might find fruit trees being sold off cheap at this time of year - leave them in pots or put them in the ground and use them as trellis for any of the climbing plants above - I combine apple and nasturtiums in a hedge which works quite well.
A rambling rose (like 'Rambling Rector') would work through the trees, or on a trellis - take a while to get going

The problem with fast growing trees is that they take up lots of space, and you do have to keep on top of the pruning.

Thankfully, no one got trigger happy and mentioned leylandii. If anyone does, discount it immediately.

What about a russian vine, its not called the mile a minute plant for nothing, but again it will need a trellis for support.

A thing that grows fast will need a vast amount of cutting back every year. Russian vine and similar fast-growers will form a tangled mass of branches and twigs the size of a garage.

Reconsider using trellis.

If you have garden soil under or beside it, you can grow an annual screen of such things as sweet peas, french beans which will grow quickly and die back in winter. Or grape vines which are pruned in winter but will regrow quickly in spring and form a mass of leaf. Presumably in winter you will not spend so much time in your deckchairs in the garden.