I'm not sure I understand your request. You're looking for a payment processor that is willing to accept casino, forex, etc. related transactions? If so, then I don't think there is a better alternative than running your own node and coding your own thing. I don't think a traditional payment processor is ideal for what you're trying to do.

They already were a payment processing business and they are only looking for partners that would use their services which as the OP have said that they already have permits from it. The question now is that would even anyone here in the forum would take a chance to risk their businesses on accepting this business offer --  in which I don't think that even anyone in this forum are onto looking for payment gateways as there are already tons of reputative platforms that has the same business idea.

You should use the social media we have now in our time, aside from that, you can also post your promotion here in the forum
in the right section thread. Anyway, I do hope that you can help a lot of community here as well, and good luck to your project campaign
in the future.

You can add a Facebook Groups to your Promotion Plan

You can try in and spend some btc in bounty thread to announce your exchange. You can also try other advertising platform such as google adsense, or brave. So far using brave more efficient and cheaper than adsense

Any advertising should be rewarded at its true worth, and therefore the resource can conduct a referral program for its users, as well as use quite ordinary companies such as an airdrop or Bounty company, in order not only to spread information about the exchanger, but also to attract new users for which you need to come up with special bonuses and lotteries to make them want to stay.

Hello!
I think you already got many good answers, my only inquiry is what makes your exchange unique? These days theres as many exchanges as there are shitcoins therefore making marketing harder since why would a client of a well known exchange he uses, switch to some new exchange which does the same?

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An Affiliate Marketing program would be good. I have seen almost every exchange have their Affiliate Program and they work pretty well for them as their existing users refer their friends and promote the project everywhere to gain referral and earn a commission.

If you have some active users then starting a referral program would be a nice move towards getting more customers to your exchange.

if you start an affliate marketing program with Good Referral reward (more than 20%) then I might work for you to promote your project. I have been doing affliate marketing of Binance and some other legit exchanges.

you can also check out my website if you need other digital marketing help:

https://coinfluencers.co

With that question, you have a lot of options.

If you want to start it outside on this forum.
1. Find a popular model.
2. Advertise your product.
3. Make a beta test for your users.
4. Be unique to other exchange platforms.
5. Promote the use of different media platforms like Television, radio, and more. But right now we have the social media to make it easier to access with this exchange.

If you want to run with this our forum you can make
1. Announcement board or thread (ANN)
2. Run a signature campaign.
3. Make an event to your platform like bug hunting.

I guessed we already got the point here since the OP got their exchange to have an Estonian License with it I doubt that they are looking for free ways of promoting their website because if they will just rely on their friends and family to post tweets and retweets I doubt that it would have the same affect as promotions actually coming from ad pages. This kind of advertisement will only make them "scammy" looking as what people generally see on crypto related advertisements coming from people they know. Like what I said on my first post in this thread if they want to have the right audience its best for them to pick crypto ad networks to promote their banners for their site.

Launch a decent announcement thread complete with a good design I also recommended that you complete all your social media sites, and build your telegram or chat channel so they will know where they can reach you if you have a budget launch a signature campaign this is for awareness, it's actually word of the mouth that will attract you more users, so improve your support.

To be honest, you have a team and now you are asking how to market the platform This doesn't sound very trustworthy and doesn't sound like professionals are going to run the exchange. Running an exchange is a highly complex matter. Whoever then asks for marketing tips will surely fail.

Do you think that buying slots on this kind big websites is a good idea? Maybe much better will be spend this money on ads at Social networks?

Running an advertising campaign on Facebook and Google can help a lot. They are holding a great amount of customer's insight in which you can use and make a suitable target. The signature campaign is also a great choice for sponsors cause the bitcointalk community is a place where most of the crypto traders come to visit. News and articles are also very good but you need to have the right source with a high volume of traffic daily. I suggest you can make an offer with Coindesk. Many traders read this site for new information

You can start by posting the name of your exchange here.
https://revalcoin.com/en 

Next job would be to start a bitcointalk signature campaign like OSS said.
As I understand it is just a list of verified services and so on, right? How to list our exchange there?

Then go for promotional content on news media sites like cointelegraph and others. Some managers here might be able to link you up with them for a sweet deal so make sure to ask them first.

Where I can find the contacts of this managers?

Thanks! 

Sponsored and guest blog posts can also help.

You mean influencers and bloggers on YT and so on?

Forget Facebook, it's full of low information voters. You can use it for your profile but don't waste resources on it.
What do you mean by low information voters?