Is it an Instagram influencer? If so you could just post your own forum links and stuff on Instagram and tag the influencer and various other people and subjects

My forum has an Instagram account and a youtube account - it gets it a bit of publicity, but to be honest, it doesn't really gain any members from it. Just a bit of publicity. The youtube one does a bit maybe, depending on the type of video.
An influencer should do it without money - like a mutual thing where you mention them occasionally. If you're going to pay for anything I would take out a google ad. I did that initially for about 3 months and it meant the forum came top of google all the time via the ad (until it got there naturally). And that did make a difference for people finding it and joining.
I'd focus on getting it to the top of google quickly as well, by writing a lot of posts, articles and informative pieces, and backlinking them in a lot of places. You can backlink on your own youtube channel as well. Spotify is a good backlink if you open a forum spotify account too. Others are Flickr, Discord, Reddit, Instagram, Facebook, Blogger, Medium, Bluesky, X, Pinterest Quora - open accounts and most accounts allow you to add your web address.
Every long piece or article you make, share it on these sites, via the forum share icons (or directly). It's a bit of work to start with. That and a google ad.
I started with 3 members. Within a few months I had 50. Once those 50 start posting, more and more posts show up on google.
If you actually are going to pay an influencer, no more than £20! Have they named a price? If so it will be a silly price. A website published an article about my forum after I asked - sometimes they ask for a backlink somewhere on your forum - although be careful doing that more than once or twice, as google doesn't like it.