There are a large number of plants that you could use for screening around the two-to-three metre mark.
Here are just a few suggestions:
We’ve been recommended to use a conifer like Junipersas Spartan as a screening plant along a fenceline. I’m not sure I like the look and it sounds like we’ll have to be patient as it can take a while to reach the kind of height we’re after – two to three metres. Happy to hear further suggestions. - greygardener
This is what you get with a conifer - a very traditional looking hedge. I would imagine that a lot of people would recommend a pittosporum as they are fast growing - up to a metre a year. For screening you just want one that is sturdy and grows upright as well as bushing out. - Kermit
Another option you might like to consider is an ornamental pear. They are popular because they are tough, fast growing and look great. They also tend to grow at a uniform rate so are great for planting in a row. - Kellie
Port wine magnolias (Michelia or Magnolia figo) are one of my all-time favourite plants. Use them as shrubs, hedges, large topiary or small feature trees; they are just excellent and super hardy. They'll survive in most positions & conditions but do best in a sunny sort of spot with good soil.
They won't take well to cold conditions though so if you get regular frosts they may not be the ideal choice. Some say not to plant them if temperatures drop below 0˚ but I have had them in gardens that do get light frost & haven't had any issues. They make an excellent screen or hedge, very dense, but the trick is pruning tip-prune early and often to keep them nice and bushy.
Although they prefer good sun you'll find they do quite well in part-sun or even lightly shady spots too but will need more pruning to keep them dense. – Adam_W
Tip pruning port wine magnolias is very important to get and keep the plants in check so they bush up rather than head for the sky! Keep in mind the trees might need some wind protection (hot and cold) until they're established. - Noelle
We have many beautiful examples of sesanquas used for hedging down our way. - suequarford
I have an established line of magnolias along my front (north side) fence on Sydney's Northern Beaches (not right on the coast). Unfortunately, I hadn't picked up the advice about regular tip pruning to get bushiness. The result is that we now have 2.5m high and a bit sparse around the lower branches. - boatbloke
You can tip prune the top growth to encourage side growth lower down to fill the plants out, but it may take a couple of years to achieve the look you're after. Magnolias have a tendency to produce strong upright shoots if pruned too severely, so don't go in hard.
Take out the top 30cm or so of the main upright shoots now, and then next winter repeat that pruning technique to force the trees to produce more side shoots next spring. You might not be able to get them to fill out right down low but they will certainly look better for the effort you put in. Regular tip pruning through the growing season is best - nipping off just the growing tips.
Another path is to put up a substantial trellis along the entire fence - concretors' reo/reinforcing mesh) is ideal - and training climbers over it. Star Jasmine, Potato Vine and any other fast growing climbers would be ideal. Regular trimming will keep them neat and still allow you access even in a narrow passageway between a house and fence. - Noelle