But if my lane carry doesn't have any issues with enemy on our lane... What should I do as a support in this situation?
You will almost never be in this situation. The thing you have to remember is that the second you leave your ADC alone in lane, he is now in a 1v2 situation. If the opposing botlane is at all competent, they will abuse their advantage mercilessly. It doesn't matter what kind of botlane they have (kill/poke/sustain), in a 2v1 situation they will push your ADC off the wave and prevent him from farming. If your ADC greeds for the farm, he'll most likely die. Both scenarios are a good way to start flame wars.
If your ADC is pushed to his tower in a 1v2 then he might be okay for a short while. However, most botlanes can then poke him down to the point that he has to leave or they'll dive him, with or without jungler support depending on their comp.
Short roams to mid or jungle to gank or invade can be useful but also leave your carry stranded so should only be done when he's recalling or can be relied upon to survive until you return.
The only situation in which you should truly leave botlane is when the ADC tells you to (for instance when he's freezing) or when you know he can take a 1v2. The latter will generally only happen when your carry is hyperfed and significantly more skilled than their botlane. Many botlanes can still combo a fed solo ADC who's out of position. You should also only do this if the potential rewards outweigh what you could do in the botlane. Don't leave your lane if you can easily kill their botlane again or deny them farm.
I'm answering from experience here. I routinely support a high-diamond ADC main in group games with friends from all skill levels. This usually means that our ADC does get hyperfed but it's very rare that he will be confident enough that he can outplay two people. Leaving a fed ADC alone so that he can't farm or can be easily ganked is a great way to trow your lead and piss off your teammate.
Or as this particular ADC main said upon learning of this question:
Honestly if you find playing support boring: don't play it. All you'll do is irritate your adc by running around trying to force fights.
If you do ever happen to be in this situation, typical things to do are to accompany the jungler in ganks, camp top/mid or invade to secure vision if you have the kit to survive that. By the time you reach this point the laning phase will typically be over anyway.