There are a lot of treatments available for teak and an equal number of people that like one product or another. I think you can find discussions on almost all of them here in other threads.
If it has a finish on it already and it isn't looking good it means the UV has destroyed the finish. All finishes reach that point sooner or later. Some are easier to remove than others and some more work
to apply. The harder it is to apply the harder it comes off when the time comes. The easiest application material needs to be repeated much more often. I think you may find over a long enough period that it all takes the same amount of time if you add up all the hours.
You can start with 60 grit sand paper and remove the rest of the finish taking care not to scratch the gel coat. As the finish comes off new wood
is exposed and you should see the nice rich warm glow of teak. It turns silver if left untreated in a few weeks.
Teak trim can split as it dries out from prolonged exposure to the sun. It really can't be repaired once that happens.
Find something you like the look of and pay your dues like the rest of us. Time on the boat
maintaining teak is therapeutic. I'm just not sure what it is therapeutic for yet. I know it boosts the sales of muscle ache remedies.