Your points will reset to 0 at the beginning of each month. You can then start claiming all the rewards again starting from Bronze Tier. You will still keep your current Tier and Points Multiplier in order to boost your progress through the Clubhouse.
For example:
During January you collected 30 500 points and reached the Gold Tier. On February 1st your points will reset and you still remain in the Gold Tier with a 1.25x points multiplier. In order to stay in Gold Tier for March you need to collect at least 30 000 points in February.
To see how many points is required for each Tier, click here.