Access to climbing areas is an ongoing issue in many climbing areas. In the United States for example, it is claimed that 1 in 5 climbing areas is threatened by an access issue. There are many funds, societies, and advocacy groups who work on behalf of climbers to protect public access to climbing areas, to keep them open to the public for recreational climbing. Try searching for an access group that works in your area.
The issue of access is not always so simple, as there can be multiple factors to consider when it comes to certain crags. Around where I'm from, there's pretty much open access to everything, because most of the climbing areas are on crown land. There are however a lot of cliffs and boulders that are on private land, and private land owners have the right to prohibit trespassing on their property.
The biggest concern with climbing on private property in some countries is liability. In North America for example, If someone gets hurt climbing a private crag, then the landowner is legally liable, and can be sued. Most land owners prefer to restrict access to their lands instead of risking the possibility of even one lawsuit. Local authorities are especially likely to restrict climbing on municipally owned lands, because they are regularly subject to a plethora of ridiculous claims (people frequently sue towns and cities because they can't be bothered to be accountable for tripping over their own feet on the sidewalks, and hurting themselves). In the USA this is especially common because in many cases suing is the only option an injured person has for paying their hospital bills.
One sensitive issue with a lot of climbing areas is the presence of native art on the rocks. I know of several areas nearby that are prime climbing areas, but climbing there is somewhat controversial because it can do damage to the ancient art on the stone. Access to areas where native art is present is often restricted, and it just so happens that in most places where native art is preserved on stone, the rock is prime for climbing.
If climbing has been banned at your crag "for safety reasons" then it sounds like a local authority issue, in which case your best chance of restoring access is to partner with a access group, and petition the local authority. If you can show the authority that an area can be responsibly climbed, then they may work with you to open access to climbing. Talk to the CAO or City Manager about presenting to your council, that should always be your first course of action when seeking change in a policy in a municipality.
As far as preventing access issues, what you need to do is demonstrate that the area is being used responsibly. Leave No Trace ethics will ensure that no flags are raised about improper use of an area. I've seen crags full of garbage and covered with graffiti.
There's a now-popular climbing area close to where I live that used to be closed to climbing. The Town of Frank in Alberta used to prohibit people from climbing on the millions of boulders which were the result of the worlds largest rock avalanche, that buried most of the Town early in the 20th century. I remember when signs used to be posted on the side of the road telling you that climbing on the rocks was prohibited. Today it's a renowned bouldering area with thousands of established problems, with more new problems being established almost weekly. Access was granted after it became clear to the municipality that bouldering was a huge tourist attraction, and promoting the area attracts a lot of tourism and benefits local businesses.
Frank Slide (Gripped Magazine)