Separate finished tea from its leaves
An infusion stops changing through leaf contact only when liquid and leaves are separated. Use a removable filter or a second vessel to make that endpoint clear.

A strainer at the spout is not an off switch
A pot can pour beautifully clear tea while the leaves remain inside it. The spout filter prevents leaf pieces reaching the cup, but it does not remove the leaves from the water left in the pot. If you serve one cup and leave the rest for later, that remaining portion continues brewing. The last cup may therefore taste quite different from the first even though neither contains visible leaves.
For a clear endpoint, either lift out a removable basket or pour the whole infusion into another suitable vessel. Choose a receiving pitcher with enough capacity and set it close to the pot on a stable surface. A separate strainer can catch leaves during the transfer if needed. Keep the strainer secure rather than trying to balance it with one hand while managing a heavy full pot with the other.
Decant when the tea is ready
Have the receiving vessel ready before the timer sounds. Pour in a controlled stream, keeping your grip comfortable and the lid secure. The tea continues contacting the leaves during drainage, so a very slow pour is part of the total brewing process. If the spout repeatedly clogs, inspect the cooled pot and consider a more suitable filter or leaf size for that vessel.
For a single mug, removing the basket accomplishes the same separation without an extra pitcher. Place the wet filter on a drip dish and avoid letting the basket sit back down in pooled liquid if you intend another immediate infusion. The details of the equipment differ, but the purpose remains simple: finished tea on one side, wet leaves on the other.
Holding and reheating are separate decisions
After separation, the tea will still cool and its aroma may change as it stands, but it is no longer extracting from the leaves. Use a clean suitable serving vessel and drink it within a sensible fresh serving routine rather than leaving it warm for hours. If you need tea for a journey, follow the flask's instructions and fill it with strained tea. Keeping leaves inside an insulated bottle can make a carefully timed brew continue far beyond the point at which you liked it.