First, check when the rink offers public sessions that you can practice on. Even if you can only get there once a week, try to plan your time so that you can have an hour or more on the ice at each visit.
Have you been taking group lessons? The instructor, or the skating director at the rink, should be able to advise you about the available practice and lesson times.
If you can continue taking lessons, you will continue to learn new skills, but you always need to keep practicing the skills you've already learned to improve them and be ready to add new skills that build on the previous ones.
Are you in the US?
Are the group lessons at your rink offered through US Figure Skating or through ISI or their own curriculum. If USFS or ISI, you will probably need a learn-to-skate membership through those organizations.
You can move up the levels of the group classes as you master the skills at each level. If you are interested in competing at these levels, look for "Compete With Us" or ISI competitions held at rinks near you. The group instructors should be able to help. But preparing for competitions takes more time on the ice, and often some private lessons, in addition to just learning and practicing individual skills. There's no need to rush into competing, but do be aware that there are opportunities to do so at beginning levels if that is of interest to you.
Joining US Figure Skating as a full member, usually through a local club, in most cases is not necessary until you are ready to take the first formal Skating Skills test, the Pre-Preliminary level.
Here's an example of a coach demonstrating the moves you will need for that test:
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You can search youtube for "Pre-Preliminary Moves in the Field" (the name for this test track just changed from Moves in the Field to Skating Skills at the beginning of this month) to see examples of the level of ability skaters usually have when they take this test.
If you're just taking group lessons and practicing once a week, it will take you some time to reach that level, but it should be an achievable goal to aim for.
If you can skate more often and take some private lessons as well, you could get there more quickly. But this requires more money as well as more time on the ice and more weekly trips to the rink, which would also be needed to move on to more advance skills and tests/competition.
US Figure Skating offers beginner competition opportunities at their regular competitions for skaters who have started to master the first jumps and spins. It is possible to enter those competitions at that level with just a Learn-to-Skate membership without club membership.
The only reason you might want to join a local USFS club sooner might be if the local club offers ice time that is appropriate for beginners to skate on at your level at times that are more convenient than public sessions or group lessons run by the rink.
Other clubs only offer ice time for skaters who have reached a skill level toward the end of what the learn-to-skate classes teach.
You can see if the local club has a website that would answer some questions about what they offer and provide contact info for a club representative who could give you more information.
Again, the group instructors should be able to point you toward how to contact the local club when you're ready.
Skating clubs are for all ages, although some small clubs may only have skating members in a more limited age range.
If there is an active USFS club in your area, there are probably some teens who participate at a more advanced level.
Some clubs also offer off-ice social opportunities, or sponsor test sessions, shows, or competitions that you could volunteer at even before you're ready to participate yourself.
If you are still a minor when you're ready to join a club, you may need to have a parent join as a parent member, which may be free if they don't skate themselves. Your skating membership will have an associated fee.
Check with the local club when you're ready. But there's no rush to join a club while you're still working on learning beginning skills.
Have fun!