Warm welcome to the forum.
Basil is an annual. That does not mean that it will last for a year. A annual will last one season.
The life cycle of an annual is to grow, produce foliage, flower, go to seed then die.
You may be able to fool mother nature for a little while but in the long run she wins.
In your region your basil season is summer. You can extend that a little bit by pruning but your best bet is to start new plants for each season.
Of course you will need to grow fall, winter and early spring basil inside with adequate light. You will need an artificial light source.
Take cuttings now. 3 or 4 3" - 4" cuttings. A good way to start is to use 4" nursery pots. You can get them free from your big box stores and local nurseries. They cull distressed plants and toss them with the pots. Ask for the Nursery Specialist or Department Manager at the big box store. Ask when they cull plants and let them know that you need a few 4" pots. Wash the post in a sink of hot water with 1/4 cup bleach. Rinse well.
Plant your cuttings in the pots filled with all purpose potting soil - no fertilizer needed. Leave the cuttings outside until the temperature gets close to 40 degrees F. Keep the soil evenly moist - not soggy. That will entail daily watering. Your cuttings will have a root system in 2 - 3 months. The plants will put out new growth when the root system is established.
When the temperature starts to drop move them inside. You need a shelf or shelving unit with adjustable shelves and shelves that drain. Use shop light fixtures with grow lights. Big Box store.
Let the rest of the basil flower and go to seed. Collect the seed. Use the seed to start plants for the next season.
In south Louisiana I plant Basil starts in March (seeds started in January). The starts are planted outside in the herb bed. By mid June they are going to seed. I plant 2 or 3 starts in May. Plant in late June early July. I also harvest seed. Late summer is very hot and basil does not last long so I start seed in mid June. They will be ready to plant in August. Those plants can last for several months depending on the weather. I do not plant winter pots for indoors. I always have basil butter, basil infused Olive oil, dried basil and frozen basil.
Sorry for going on so long. Take and plant cuttings and harvest seeds. Harvest leaves ad at least dry what you have.
Looking forward to hearing more from you.